This is the type of math teacher I like. The teacher who actually lets their kids understand the math instead of making them pass the exam so he doesn’t have to worry about it again.
I am a math and computer science major and a math teacher (middle school) and, like others have commented, I have never seen this method before. I love how you can easily get non-integer solution sets! Perhaps instead of the "Po-Shen Method" I shall henceforth call this the "Magic Quadratic Po-Shen" (just to add a little wordplay)!
This is one of the best lectures on quadratic equations I have seen. Thank you Mr Loh for clear and understandable information presented in a concise manner.
I salute you man! This is absolutely amazing....have been teaching math for 35 years, you have just made my job easier for whatever remaining number of years I will be able to teach. That's why they say....it doesn't matter you learned something new so late in life, what matters is you got new knowledge (new, I say, for the learner), new wisdom. And last but not the least, what is the primary objective of Problem solving....in any branch of knowledge or education....it is to achieve the objective in as simple and as uncomplicated a manner as possible....so that it can bring a smile on the faces of our students. Thanks a zillion bro!!!
@@muhammadazeem9775 Just a tip, based on my personal preference. I almost never click on a video link that does not include a brief statement of what the content/summary of that video is...you'll attract more clicks with a brief statement. Nice rose picture.
I have been teaching this method to my high school students back in 1999 and yes, this is another way. Students will definitely learn if a teacher will expose them to different ways of solving the problem. Nice presentation...
I realise that this is basically not much different than completing the square. Why was this method not widespread before? It would have saved many students a whole lot of suffering...
@@geraldillo The one thing I don't like about this method relative to completing the square is that it doesn't teach the "add and subtract" trick, which is useful elsewhere in math. To clarify what I mean, I think of completing the square in this kind of format: x^2+2x+2=x^2+2x+1-1+2=(x+1)^2+1. The "I can just put a +1 there as long as I take it away later" concept is kind of magical to an algebra student, but is widely used elsewhere in math. Unfortunately I sometimes see students learning this in terms of adding the desired quantity to both sides of an *equation* which is really the less common way to think about it in more advanced math.
I’m reviewing all of my precalculus math that I had 50 years (!) ago. I wish I’d had you for a math teacher back then. Thank you so much for the teaching an old dog a new trick! I’m planning to learn a lot more new tricks. I’ll be watching more of your videos in the future! Thanks so much!!
This is exactly how we learned in my country East Africa. God how did I forget this, and our professor has zero clue and got me confused and spent days to really figure this out. I wish I found you early. I would have saved a lot of time. But thank you so much! You did an amazing job. keep them coming.
Haven't you taught your students one of the methods in finding for the roots of a quadratic equations is by completing the perfect square trinomial? This method is used how we arrived at the so-called quadratic formula😀
@@jecelaguilar9319 At first, I didn't get what he was doing. So, I Completed The Square on a couple of problems, using an area model. I'm a really visual and conceptual math learner, so things like area models really help me. After I did some problems, I realized that his method is basically a shortcut for Completing The Square. I had the idea because he said his method always works. To those of us in the U.S., this approach seems different because it's not the exact way we are taught to Complete The Square in school.
This is so elegant, intuitive, and forces the solver to think about what's happening and how things relate to each other. I wish I had TH-cam back when I was in school.
I actually watched the 40:05 minute video without skipping!😂 Just like learning golf, when you can connect with the instructor through the way the knowledge is properly conveyed, then you find gold at the end of the rainbow!🎉😊
You are simply great. I have never seen such a pleasant mathematics teacher during my learning period. I am now 72. Today you taught me a novel technique. I salute you
Dear Prof Loh, I am now retired at 61, and I have worked in IT for most of my working life. I have, however, always dabbled in mathematics. The thrill of discovering this only recently, is one the reasons for my continued love of the subject. If you have not done so, adding the graphical interpretation would help many other students. Thank you very much.
What a joy that this method fits naturally in each number domain! The intuition of "finding the average" leads so smoothly into creating a complex conjugate pair. It's as if we knew more than we knew we knew, all along. Thanks for sharing this so well!
As a 4th grade teacher, I can tell you that it would be incredible to have this kind of talent exposed to the kids right from 1st grade on. So much of the math problems we have is because we lack our natural curiosity and stop having fun. Math gets to be all about 'testing' pretty quick once they leave 6th grade. Thanks for posting, great lesson.
Thank you for sharing your thoughts! Math is about reasoning, not about memorizing. Everything in math can be taught in a way which illuminates the reasons. :)
Po-Shen Loh yes! It’s no good to just memorize. That will be quickly lost. But the ability to explain your way through a concept gives access to so much more.
Mind Blown! Genious! Not just in the solution but in the expert EXPLAINATION, very clear and understandable, just amazing! Thank you for taking the time to produce this video. I will go over it several times to make sure I understand its simplicity. I am now a follower and will look over your other videos. Wow, just amazing how ancient secrets from hundreds and thousands of years ago are lost over time but come back to life. I wonder how many other things are like this?
This was amazing! I actually had to pause the video and derive the quadratic formula because I was so excited about noticing how it relates to this method. As soon as I finished I unpaused the video and Professor Loh started talking about how to use the method to derive the quadratic formula. The logical pathway is so satisfying in this video and I am grateful to finally understand the quadratic formula!
thanks Po-Shen Loh, I never studied this method in school or in University but I'm so thankful for sharing your knowledge and understanding of different methods to solve quadratic equations. I prefer learning this method for all students to know is the best choice than the normal way. Glad how you ended up connecting or even linking to the Quadratic Formula itself.
Great method! It's so rare you see an improvement over such a basic thing as quadratic equations. I just love your enthusiasm. Science Alert brought me here.
Just to make it clear, the method presented in this video is not new in any way. It is just a relabeled version of the well known PQ-formula being taught to high school students all around the world. The algorithm in the beginning is just a common derivation of it. However, there is nothing wrong with the video it self. It is one of the most pedagogical videos on quadratic equations I have seen, good job on that.
Teachers like you and my best maths teachers(Chandan Sir,Azizul Sir)really inspire the students to discover and love the maths.Much respect to every good and ideal teachers.
Genius! Why did we not learn this method at school seeing it has been known for hundreds of years. If we had more of these techniques in math classes there would be a greater interest in mathematics and more people will pursue mathematics as a career.
The method at 00:46 is just the quadratic formula. - B/2A +- u, where u^2 = B^2/4 - AC. The x-coordinate of the vertex of a parabola is -B/2A. It is also the line of symmetry. If you extend the line of symmetry through the x-axis, you will see that one root is a distance SQRT(B^2 - 4AC) to the right and the other is a distance -SQRT(B^2 - 4AC) to the left. The method is a bit different than just plugging numbers into the quadratic formula, but there is really no new math here, just a different way to apply the quadratic formula.
This is amazing, I am watching your videos to see if they'd be a good resource for my son who's 14, but you just taught a 43 year old engineer something new! Thank you!
Many thanks for this video! It gave me (and my high school students) new insight into understanding the cubic equation formula which uses the same beautiful ideas explained so well in this video. It never crossed my mind to use these ideas to solve the simpler quadratic equation. So, thank you! Best regards, Anna/Helsinki/Finland
The Indian mathematician Brahmagupta (597-668 AD) explicitly described the quadratic formula in his treatise Brāhmasphuṭasiddhānta published in 628 AD,[24] but written in words instead of symbols.[25] His solution of the quadratic equation ax2 + bx = c was as follows: "To the absolute number multiplied by four times the [coefficient of the] square, add the square of the [coefficient of the] middle term; the square root of the same, less the [coefficient of the] middle term, being divided by twice the [coefficient of the] square is the value."
Awesome method! I am physics student and even though I am very familiar with quadratics I always find the quadratic equation and factoring very tedious! Your method is much faster.
He's actually "completing the square"! Throw the constant on the other side as a negative, take half of b, square that and add it to the number on the other side. Then you take plus or minus the square root, then add the number from the left side. I was actually thinking along those lines a few weeks ago, but didn't have time to follow it through. Hats off to you!
Thank you for your fantastic teaching skills. I'm very happy with your lessons, because it's so easy, but I don't know why they don't teach us in College like this beautiful way. Thanks a lot.
All indians must have studied it.. It's called Shree Dhara Acharya formula. But this is the first time i have understood the essence of the formula. That's why it's imp to understand the proof of a formula or how a formula came..this may make students buildup an interest in Mathematics. Loved it👏
Thank you sir. It's a brilliant way of solving quadratic equations rather than memorising the quadratic formula. Hoping for you to come up with many other tricks to simplify Math
Dr. Loh: The technique of completing the square and its formal form, the quadratic formula, are beautifully re-interpreted to present an easy to handle method. Will always love to tell my students this method, giving your reference (Dr Poh-Shen Loh) and encouraging them to watch on the TH-cam.
Thank you so much! I'm studying for the GMAT right now and this method is going to help me work through quant problems involving quadratic equations much more quickly and efficiently!!
I'm a little surprised that this is considered a novel thing in the US. I learned this as the "standard" method for solving quadratic equations in junior high in China. But Prof. Loh still kept me engaged. Great professor!
we did this thing called the quadratic formula that enabled us to solve any quadratic equation in Hong Kong. if i remember correctly, it was (-b+/-(b^2-4ac)^1/2)/2a if u do manage to remember it, solving quadratic equations is quite simple as well
Thank you very much sir for this wonderful method. I m an indian JEE ASPIRANT and even i m very thankful for this method. I really going to share it with my friends.
Showed this to my 7 year old math obsessed daughter and she immediately understood. She loves learning advanced math and we love your explanations. Thank you!
Love this clever use of dimension reduction. A = x + y -> A = (A/2 + u) + (A/2 - u). I also found a fun little generalization: If A = Sum ( x_i ) for i = 1, 2, ... , N then let x_i = (1/N)A + iu for i < N and x_N = (1 / N)A - ((N - 1)N / 2)u. One number is the counterweight and the rest are various multiples of u.
Are you suggesting that this can be used to factorise cubics (N=3) and higher order polynomials? If so, then how does your method work? If not, then what is this a "generalisation" of?
Po-Shen Loh, I know you are deservingly happy discovering that we can find quadratic roots much simpler by combining these two ancient insights, BUT have you taken the time yet to notice the other side of what you have discovered? A new insight. Yes, the roots do exist but you have more importantly shown that the average of the roots also ALWAYS EXISTS! And we now see a new and strange average of the roots for an equation like x^2 -2x+3 for example yet see similarities of the root averages of X^2 +1 and horizontal translation of it like x^2 -2x +2. This is the new Loh insight of complex root averages and/or complex averages in general.
This is really cool. You can actually use this to derive the more commonly known quadratic formula. Just keep the variables, start simplifying and rearranging, and eventually you end up with something in the exact same form as the quadratic formula. Would really love to see you show the 2c form of the quadratic formula. It can be easily derived with simple algebra by taking a quadratic equal to 0, subtracting `c` on both sides, and dividing by `ax + b` to get `-c/(ax + b) = x`. Then, substituting x for the quadratic formula. After simplifying, you get a new quadratic formula (which can even solve lines!) which is equivalent to the original but flipped (reciprocal) and the 2a becomes 2c. Additionally, the `-c/(ax + b) = x` form you might note sorta looks recursive, and you can use it to solve a whole set of simple continued fractions (e.g. the one for phi aka the golden ration, the square root of two, etc). It basically shows that quadratic equations are continued fractions too! It's very cool. I discovered both in my senior year of highschool.
Most helpful video I hv ever seen in u tube...literally For 10th grade indians.. it's so helpful as V hv a whole ch on quadratic eqns Really V used 2 find it so difficult to factorise big numbers but now it's way easier just cuz of u Great thnx sir ✌🏼👍🏼😊
I know three ways so far: Using Quadratic formulas Sum of squares (yuck) The "x factor" don't know the technical term Now I got another way...ok, I am tired lol and thankful at the same time. You are amazing to find another way. You are a real jewel.
I think this is quite remarkable to be put into words. A lot of my family members struggle with quadratic equations and I think this will be much easier for me to teach them. To be honest, this is already kinda what I use to brute force my way through quadratic equations with very large coefficient's to impress whoever I'm tutoring at the time. This definitely takes it a step further though.
You try to impress people you are tutoring..... and in just basic algebra? LMAO, that is too funny. If you want to impress the people you tutor just do what I did; I was tutoring people in the class I was also taking, and I even tutored some people in organic chemistry, and I never even took the course. So when my fellow students find this out, they are amazed at how I know all this stuff, "Even better than the teacher!" That is true impressments
Thanks professor for very meaningful video, really love the way you express the logic and guide how to produce the result, actually in real use it will be very quick by just writing down neccesary part to calculate. And in fact i learnt 1 new trick of solving sys of equations consists of a product & a sum (the average plus/minus). Also i would like to contribute another approach for this as well: x^2 + bx + c = [x^2 + (2b/2)x + 1/4] + c - 1/4 = (x + 1/2)^2 + c - 1/4 . It's look a bit complicated but if understand how to express (a + b)^2 should be very easy to imagine. But then, just another trick, and the important is still how we understand things and utilize them the right way.
This method actually combines factoring with an understanding of palabras (the midpoint, in particular). Once you understand it, I do think it's easier. However, it works better on some problems than others. If there's a leading coefficient other than one and you have to deal with lots of fractions, things get can get messy.
I am quite surprised that this has not been more widely known. In Germany it is called the pq-Formula (because of x^2+px+q) and it has probably been the most common way it is being taught.
@JJPhenom I'm American. When I was in school, we were just expected to memorize the Quadratic Formula. It was never explained to us. I had never heard of the PQ Formula -- until I heard of the Po-Shen Loh method and began doing research and watching a lot of videos. I think the way the Po-Shen Loh method is presented (especially when done with a graph) makes it easier to understand & makes the formulas make sense.
@@jjphenom2831 I think it's because of how generations of math educators have been taught (at least in America). I've talked to a lot, and the idea of learning math on a deeper level, from a more conceptual perspective, is pretty new for us. Back-in-the-day, being good at math just meant that you were good at memorizing algorithms (even if you didn't understand them). Plus, the standards that teachers had to meet in order to teach math were pretty low. When they first raised them, many teachers that had been teaching for years, couldn't pass them. It was a big deal because they also couldn't replace all these teachers. The kids basically got screwed. These teachers were talking about how hard the tests were to pass. So, I asked some professors that had taught at the high school and college levels. They said they weren't that had -- if you understood math. If just tried to get through everything using memorization, you were in trouble.
@@chocolateangel8743 Oh I see. That sounds like an interesting shift in approaches. I will be following up on how successful this turns out to be. Here the formula is often applied quite algorithmically and without going very deep into its derivision. I do not know the reason why this is the predominant method of solving quadratic equatiins though. Would be interesting to see a worldwide distribition
wonderful,always smiling and enjoying teaching.the new approach to quadratic i missed in high school.keep up the good work and be blessed.kenians commenting.
Very good alternative non-Guessing method for absolute Beginner. But for those exprienced people, they just look at the quadratic Ax＾2 + Bx + C = 0 , immediately write out the answer within split of second before the standard formula appearing inside their mind/brain ! This is human autoreflexive actuon through repeative practicals/failures . Action is faster than the Thinking mind. It is just like Chinese Primary School that everyone must memorised 9 x 9 or 12 x 12 multiply tables! after you left Prinary school and seldom use the multiplication tabkes for 10 yrs ,20 yrs ,50 yrs .Your mind already forget all the multiplications .But whenever somebody said A X B ! You immediately give the Result Faster than your mind thinking by Instingct ! I still prefer your alternative technique when teaching Beginners/Layman ! GOOD job keep it up .
This is the type of math teacher I like. The teacher who actually lets their kids understand the math instead of making them pass the exam so he doesn’t have to worry about it again.
th-cam.com/video/L4ImyFn1xLk/w-d-xo.html
Right bro
I wish I saw this lecture before JEE exam lol. The graph method makes the questions INCREDIBLY easy
he also has an iq of like 230 so that might have something to do with it
Hmm
I am a math and computer science major and a math teacher (middle school) and, like others have commented, I have never seen this method before. I love how you can easily get non-integer solution sets! Perhaps instead of the "Po-Shen Method" I shall henceforth call this the "Magic Quadratic Po-Shen" (just to add a little wordplay)!
I saw a video in which a college professor did the same thing -- because he couldn't remember how to pronounce his name.
Portion
This is one of the best lectures on quadratic equations I have seen. Thank you Mr Loh for clear and understandable information presented in a concise manner.
Thanks for your feedback!
@@psloh sir, could you please reply me??
th-cam.com/video/L4ImyFn1xLk/w-d-xo.html
Why 14 doesn't become -14 as in x^2-14x+24, can someone explain it pl
I salute you man! This is absolutely amazing....have been teaching math for 35 years, you have just made my job easier for whatever remaining number of years I will be able to teach. That's why they say....it doesn't matter you learned something new so late in life, what matters is you got new knowledge (new, I say, for the learner), new wisdom. And last but not the least, what is the primary objective of Problem solving....in any branch of knowledge or education....it is to achieve the objective in as simple and as uncomplicated a manner as possible....so that it can bring a smile on the faces of our students. Thanks a zillion bro!!!
Sir pls do research on vedic maths which will change your life 🇮🇳🇮🇳
My teacher had me explain this to her and now she's recommending your technique and referencing to you! Thanks from Sweden!
not your but as a tip
Of course other countries know this while USA still wants kids to learn the route method
th-cam.com/video/L4ImyFn1xLk/w-d-xo.html
@@muhammadazeem9775 Just a tip, based on my personal preference. I almost never click on a video link that does not include a brief statement of what the content/summary of that video is...you'll attract more clicks with a brief statement. Nice rose picture.
I have been teaching this method to my high school students back in 1999 and yes, this is another way. Students will definitely learn if a teacher will expose them to different ways of solving the problem. Nice presentation...
I realise that this is basically not much different than completing the square. Why was this method not widespread before? It would have saved many students a whole lot of suffering...
@@geraldillo The one thing I don't like about this method relative to completing the square is that it doesn't teach the "add and subtract" trick, which is useful elsewhere in math. To clarify what I mean, I think of completing the square in this kind of format: x^2+2x+2=x^2+2x+1-1+2=(x+1)^2+1. The "I can just put a +1 there as long as I take it away later" concept is kind of magical to an algebra student, but is widely used elsewhere in math. Unfortunately I sometimes see students learning this in terms of adding the desired quantity to both sides of an *equation* which is really the less common way to think about it in more advanced math.
Sir please keep posting such methods so that people start analyzing mathematics and taste the true essence of it, Thank you so much for sharing this🙏.
:)
Thank you from my 19 person math class who enjoyed learning this method
That is the easiest method I have ever used. I can't imagine that I did not know this before. Thank you sir
Google PQ
I think the Colombian Method is easier to be honest.
DominicanOps what Is the colombian method?
@
th-cam.com/video/jcRW2R42azE/w-d-xo.html
th-cam.com/video/tRblwTsX6hQ/w-d-xo.html
TH-camrs discovered it years ago
I watched this entire video without getting bored or wanting to click off. This proves that this video is godly
I wish we could have learnt all subjects this way in school. So systematically and brilliantly explained
I’m reviewing all of my precalculus math that I had 50 years (!) ago. I wish I’d had you for a math teacher back then. Thank you so much for the teaching an old dog a new trick! I’m planning to learn a lot more new tricks. I’ll be watching more of your videos in the future! Thanks so much!!
This is exactly how we learned in my country East Africa. God how did I forget this, and our professor has zero clue and got me confused and spent days to really figure this out. I wish I found you early. I would have saved a lot of time. But thank you so much! You did an amazing job. keep them coming.
What a marvellous lecture in every way! Not just a genius new method for solving quadratic equations, but also clear and precisely presented.
I have never seen this method. Beautiful. Thank you. Retired math teacher.
Thank you for your career of teaching!
th-cam.com/video/L4ImyFn1xLk/w-d-xo.html
Haven't you taught your students one of the methods in finding for the roots of a quadratic equations is by completing the perfect square trinomial? This method is used how we arrived at the so-called quadratic formula😀
@@jecelaguilar9319 At first, I didn't get what he was doing. So, I Completed The Square on a couple of problems, using an area model. I'm a really visual and conceptual math learner, so things like area models really help me. After I did some problems, I realized that his method is basically a shortcut for Completing The Square. I had the idea because he said his method always works. To those of us in the U.S., this approach seems different because it's not the exact way we are taught to Complete The Square in school.
shoutout to people like this on youtube for carrying us through school single-handedly. THANKYOU
This is so elegant, intuitive, and forces the solver to think about what's happening and how things relate to each other. I wish I had TH-cam back when I was in school.
If there were TH-cam when I was in school, I would never have gone to school. Attendance and tuition would have been a waste of resources.
VIO stand your life.
I actually watched the 40:05 minute video without skipping!😂 Just like learning golf, when you can connect with the instructor through the way the knowledge is properly conveyed, then you find gold at the end of the rainbow!🎉😊
You are simply great.
I have never seen such a pleasant mathematics teacher during my learning period. I am now 72. Today you taught me a novel technique. I salute you
Dear Prof Loh, I am now retired at 61, and I have worked in IT for most of my working life. I have, however, always dabbled in mathematics. The thrill of discovering this only recently, is one the reasons for my continued love of the subject. If you have not done so, adding the graphical interpretation would help many other students. Thank you very much.
Could we try it on Desmos?
@@southernkatrina8161 Desmos?
Desmos is a free download app that takes a function and graphs it. It's good fun and helps learning.
I had to find videos that explained it, graphically, in order to fully understand what was going on.
Every highschool teacher should learn this method
Yes
True talk
th-cam.com/video/L4ImyFn1xLk/w-d-xo.html
X²+6x-27=0
No plssss. This is complicated 😭😭 like why can't we just use the quadractic formula. It isn't that difficult to remember 😔
What a joy that this method fits naturally in each number domain! The intuition of "finding the average" leads so smoothly into creating a complex conjugate pair. It's as if we knew more than we knew we knew, all along. Thanks for sharing this so well!
As a 4th grade teacher, I can tell you that it would be incredible to have this kind of talent exposed to the kids right from 1st grade on. So much of the math problems we have is because we lack our natural curiosity and stop having fun. Math gets to be all about 'testing' pretty quick once they leave 6th grade. Thanks for posting, great lesson.
You could teach them!
I love the way he teaches, how he anticipates future content, let’s viewers know there is a reason for doing something, his enthusiasm.
Thank you for sharing your thoughts! Math is about reasoning, not about memorizing. Everything in math can be taught in a way which illuminates the reasons. :)
Po-Shen Loh yes! It’s no good to just memorize. That will be quickly lost. But the ability to explain your way through a concept gives access to so much more.
@@belmer73 :)
Mind Blown! Genious! Not just in the solution but in the expert EXPLAINATION, very clear and understandable, just amazing! Thank you for taking the time to produce this video. I will go over it several times to make sure I understand its simplicity. I am now a follower and will look over your other videos. Wow, just amazing how ancient secrets from hundreds and thousands of years ago are lost over time but come back to life. I wonder how many other things are like this?
more people need this in their lives
This was amazing! I actually had to pause the video and derive the quadratic formula because I was so excited about noticing how it relates to this method. As soon as I finished I unpaused the video and Professor Loh started talking about how to use the method to derive the quadratic formula. The logical pathway is so satisfying in this video and I am grateful to finally understand the quadratic formula!
Hi....
Hi Lauren and you done it at last?😉
Very interesting and amazingly explained. never imagined i should have seen this 40 min continously without stopping. Great. Love to learn more.
Damn I've never been able to solve quadratic equations with irrational solutions purely in my head but now I can.
Do your work and find some podophiles not quadratic lol
@@aaditrangnekar lmao
thanks Po-Shen Loh, I never studied this method in school or in University but I'm so thankful for sharing your knowledge and understanding of different methods to solve quadratic equations. I prefer learning this method for all students to know is the best choice than the normal way. Glad how you ended up connecting or even linking to the Quadratic Formula itself.
Great method! It's so rare you see an improvement over such a basic thing as quadratic equations. I just love your enthusiasm. Science Alert brought me here.
Just to make it clear, the method presented in this video is not new in any way. It is just a relabeled version of the well known PQ-formula being taught to high school students all around the world. The algorithm in the beginning is just a common derivation of it. However, there is nothing wrong with the video it self. It is one of the most pedagogical videos on quadratic equations I have seen, good job on that.
Teachers like you and my best maths teachers(Chandan Sir,Azizul Sir)really inspire the students to discover and love the maths.Much respect to every good and ideal teachers.
You're such a friendly person! It's a pleasure to follow your explanations, Mr. Loh.
Po-Shen Loh's enthusiasm is the best of the video
Genius! Why did we not learn this method at school seeing it has been known for hundreds of years. If we had more of these techniques in math classes there would be a greater interest in mathematics and more people will pursue mathematics as a career.
I can't believe that im finished watching this video, its amazing how Mr. PO makes math looks very interesting. Respect ❤️
The method at 00:46 is just the quadratic formula. - B/2A +- u, where u^2 = B^2/4 - AC. The x-coordinate of the vertex of a parabola is -B/2A. It is also the line of symmetry. If you extend the line of symmetry through the x-axis, you will see that one root is a distance SQRT(B^2 - 4AC) to the right and the other is a distance -SQRT(B^2 - 4AC) to the left. The method is a bit different than just plugging numbers into the quadratic formula, but there is really no new math here, just a different way to apply the quadratic formula.
No new maths but simpler maths 😊
This is actually the pq-Formula, but i never understood how it came to live. Thank you for this illuminating explaination.
This is amazing, I am watching your videos to see if they'd be a good resource for my son who's 14, but you just taught a 43 year old engineer something new! Thank you!
Many thanks for this video! It gave me (and my high school students) new insight into understanding the cubic equation formula which uses the same beautiful ideas explained so well in this video. It never crossed my mind to use these ideas to solve the simpler quadratic equation. So, thank you! Best regards, Anna/Helsinki/Finland
This is the first thing our teacher taught us to use and never waste time!
I was taught this, since class 8 in India.
What have I been learning all my life🙆🏾♀️🙆🏾♀️
This is beautiful 🔥🔥🔥
I like your teaching style. you actually explained how you arrived at a number which a lot of people don't do. Bravo!!!
This man is a LEGEND!
The Indian mathematician Brahmagupta (597-668 AD) explicitly described the quadratic formula in his treatise Brāhmasphuṭasiddhānta published in 628 AD,[24] but written in words instead of symbols.[25] His solution of the quadratic equation ax2 + bx = c was as follows: "To the absolute number multiplied by four times the [coefficient of the] square, add the square of the [coefficient of the] middle term; the square root of the same, less the [coefficient of the] middle term, being divided by twice the [coefficient of the] square is the value."
@@creativeclub2023 stfu
The brilliance of this method is only rivalled by the excellence of the presentation! WONDERFUL!!
I am from Czech republic and I know this since elementary school. It's one of the taught methods to solve cuadratic ecuations.
Same in Kenya
Awesome method! I am physics student and even though I am very familiar with quadratics I always find the quadratic equation and factoring very tedious!
Your method is much faster.
I have just one word for this "AWESOME"
He's actually "completing the square"! Throw the constant on the other side as a negative, take half of b, square that and add it to the number on the other side. Then you take plus or minus the square root, then add the number from the left side.
I was actually thinking along those lines a few weeks ago, but didn't have time to follow it through. Hats off to you!
Thank you for your fantastic teaching skills. I'm very happy with your lessons, because it's so easy, but I don't know why they don't teach us in College like this beautiful way. Thanks a lot.
Very easiest method to solve quadratic equation .It is very nice method. Thank you sir...
What clarity, elegance & humility. Thank you.
All indians must have studied it.. It's called Shree Dhara Acharya formula. But this is the first time i have understood the essence of the formula. That's why it's imp to understand the proof of a formula or how a formula came..this may make students buildup an interest in Mathematics. Loved it👏
Thank you sir. It's a brilliant way of solving quadratic equations rather than memorising the quadratic formula. Hoping for you to come up with many other tricks to simplify Math
Dr. Loh: The technique of completing the square and its formal form, the quadratic formula, are beautifully re-interpreted to present an easy to handle method. Will always love to tell my students this method, giving your reference (Dr Poh-Shen Loh) and encouraging them to watch on the TH-cam.
Thank you so much! I'm studying for the GMAT right now and this method is going to help me work through quant problems involving quadratic equations much more quickly and efficiently!!
I'm a little surprised that this is considered a novel thing in the US. I learned this as the "standard" method for solving quadratic equations in junior high in China. But Prof. Loh still kept me engaged. Great professor!
we did this thing called the quadratic formula that enabled us to solve any quadratic equation in Hong Kong.
if i remember correctly, it was (-b+/-(b^2-4ac)^1/2)/2a
if u do manage to remember it, solving quadratic equations is quite simple as well
This is why I love mathematics, 😀😀
th-cam.com/video/L4ImyFn1xLk/w-d-xo.html
This method is so much simpler than what I was taught. Bravo Prof. Loh!
Thank you very much sir for this wonderful method. I m an indian JEE ASPIRANT and even i m very thankful for this method.
I really going to share it with my friends.
But Isn't It Just Completing The Square?
@@anshumanagrawal346 it will come in handy for tricky quartic quadratic equations
@@ayushmansharma4362 oh ok thanks
Excellent Méthode Monsieur Shen Loh : une solution rapide et efficace. Merci
Showed this to my 7 year old math obsessed daughter and she immediately understood. She loves learning advanced math and we love your explanations. Thank you!
Professor Po-Shen Loh found and original insight. You are amazing!
Seeing this.. i feel like im recovering from my illness... So unreal.. thank you professor.
Love this clever use of dimension reduction. A = x + y -> A = (A/2 + u) + (A/2 - u). I also found a fun little generalization: If A = Sum ( x_i ) for i = 1, 2, ... , N then let x_i = (1/N)A + iu for i < N and x_N = (1 / N)A - ((N - 1)N / 2)u. One number is the counterweight and the rest are various multiples of u.
Are you suggesting that this can be used to factorise cubics (N=3) and higher order polynomials? If so, then how does your method work? If not, then what is this a "generalisation" of?
Thanks Mr. Loh! You're a great help to my math career and I can't wait to see more challenge videos! :)
Pleasure to share this one with everyone!
Yes..... He is a genius...
Thanks Dr.
I love Mathematics my favourite
Sir your content is highly discussed by Triangular Kamal which is really easy for all kinds of people.
th-cam.com/video/CMNDwY7q7AU/w-d-xo.html
He is the BEST teacher ever! I loved how he teaching way. Thank you!!
Can't wait to find this in text books in a few years or so.
Best teacher I have ever have.
This is a great way to approach quadratic equations...great job!
Po-Shen Loh, I know you are deservingly happy discovering that we can find quadratic roots much simpler by combining these two ancient insights, BUT have you taken the time yet to notice the other side of what you have discovered? A new insight. Yes, the roots do exist but you have more importantly shown that the average of the roots also ALWAYS EXISTS! And we now see a new and strange average of the roots for an equation like x^2 -2x+3 for example yet see similarities of the root averages of X^2 +1 and horizontal translation of it like x^2 -2x +2. This is the new Loh insight of complex root averages and/or complex averages in general.
This is amazing. This is" MIRACULOUS " that was very kind of you for sharing this. THANKS A LOT
This is an elegant way to do the quadratic formula in a step by step way without memorization (thus more intuitive and clear about the logic).
Brilliant! Very well explained. I wasn’t aware of this technique before...something different.
This is really cool. You can actually use this to derive the more commonly known quadratic formula. Just keep the variables, start simplifying and rearranging, and eventually you end up with something in the exact same form as the quadratic formula. Would really love to see you show the 2c form of the quadratic formula.
It can be easily derived with simple algebra by taking a quadratic equal to 0, subtracting `c` on both sides, and dividing by `ax + b` to get `-c/(ax + b) = x`. Then, substituting x for the quadratic formula. After simplifying, you get a new quadratic formula (which can even solve lines!) which is equivalent to the original but flipped (reciprocal) and the 2a becomes 2c.
Additionally, the `-c/(ax + b) = x` form you might note sorta looks recursive, and you can use it to solve a whole set of simple continued fractions (e.g. the one for phi aka the golden ration, the square root of two, etc). It basically shows that quadratic equations are continued fractions too! It's very cool.
I discovered both in my senior year of highschool.
Amazing! Will start showing students this too! Thank you!
Nice to connect with a fellow educator!
Po-Shen Loh yes! I’m so happy when I saw your video. Really inspiring! Thank you!
This is very helpful. Thank you Dr. Po Shen Loh for expounding our knowledge of maths in a precise way of Reasoning without guessing.
This is groundbreaking material, truly eyeopening
Most helpful video I hv ever seen in u tube...literally
For 10th grade indians.. it's so helpful as V hv a whole ch on quadratic eqns
Really V used 2 find it so difficult to factorise big numbers but now it's way easier just cuz of u
Great thnx sir ✌🏼👍🏼😊
Unbelievably easy and effective!!! Wish I knew this when I was a lot younger though he he. Thanks heaps. Cheers.
Thanks you. I hated quadratic equations, so much time taking.
This is the most helpful video i've ever seen
I know three ways so far:
Using Quadratic formulas
Sum of squares (yuck)
The "x factor" don't know the technical term
Now I got another way...ok, I am tired lol and thankful at the same time.
You are amazing to find another way. You are a real jewel.
A brilliant method brilliantly explained. Much appreciated.
What a great explanation to the how they came up with the quadratic equation. That was the best I've seen in quite a while. Thanks.
I think this is quite remarkable to be put into words. A lot of my family members struggle with quadratic equations and I think this will be much easier for me to teach them. To be honest, this is already kinda what I use to brute force my way through quadratic equations with very large coefficient's to impress whoever I'm tutoring at the time. This definitely takes it a step further though.
You try to impress people you are tutoring..... and in just basic algebra? LMAO, that is too funny. If you want to impress the people you tutor just do what I did; I was tutoring people in the class I was also taking, and I even tutored some people in organic chemistry, and I never even took the course.
So when my fellow students find this out, they are amazed at how I know all this stuff, "Even better than the teacher!" That is true impressments
Your method should be in all high school math books.
Thanks professor for very meaningful video, really love the way you express the logic and guide how to produce the result, actually in real use it will be very quick by just writing down neccesary part to calculate. And in fact i learnt 1 new trick of solving sys of equations consists of a product & a sum (the average plus/minus). Also i would like to contribute another approach for this as well: x^2 + bx + c = [x^2 + (2b/2)x + 1/4] + c - 1/4 = (x + 1/2)^2 + c - 1/4 . It's look a bit complicated but if understand how to express (a + b)^2 should be very easy to imagine. But then, just another trick, and the important is still how we understand things and utilize them the right way.
The first time I had my own way started to studying because of you
I’m going to teach this to all my peers at my community college.
A born teacher. Excellent sir.
Normal methods require quadratic formulas or completing the square.
This method combines the two which makes it easier
Splitting the middle term is also another normal method to solve Q.E
I am from India and these type of mathematics are taught to a eight standard students but I liked the lesson great job
Finally I can put factoring aside it's lot more harder guessing than not having to deal with it.
This method actually combines factoring with an understanding of palabras (the midpoint, in particular). Once you understand it, I do think it's easier. However, it works better on some problems than others. If there's a leading coefficient other than one and you have to deal with lots of fractions, things get can get messy.
Excellent!! The best in the internet about the quadratic equation
Well explained and the way that it should be teach
I am quite surprised that this has not been more widely known.
In Germany it is called the pq-Formula (because of x^2+px+q) and it has probably been the most common way it is being taught.
@JJPhenom I'm American. When I was in school, we were just expected to memorize the Quadratic Formula. It was never explained to us. I had never heard of the PQ Formula -- until I heard of the Po-Shen Loh method and began doing research and watching a lot of videos. I think the way the Po-Shen Loh method is presented (especially when done with a graph) makes it easier to understand & makes the formulas make sense.
@@chocolateangel8743 I absolutely agree. I was only surprised that this is not necessarily the way it has been taught.
@@jjphenom2831 I think it's because of how generations of math educators have been taught (at least in America). I've talked to a lot, and the idea of learning math on a deeper level, from a more conceptual perspective, is pretty new for us. Back-in-the-day, being good at math just meant that you were good at memorizing algorithms (even if you didn't understand them). Plus, the standards that teachers had to meet in order to teach math were pretty low.
When they first raised them, many teachers that had been teaching for years, couldn't pass them. It was a big deal because they also couldn't replace all these teachers. The kids basically got screwed. These teachers were talking about how hard the tests were to pass. So, I asked some professors that had taught at the high school and college levels. They said they weren't that had -- if you understood math. If just tried to get through everything using memorization, you were in trouble.
@@chocolateangel8743 Oh I see. That sounds like an interesting shift in approaches. I will be following up on how successful this turns out to be.
Here the formula is often applied quite algorithmically and without going very deep into its derivision. I do not know the reason why this is the predominant method of solving quadratic equatiins though. Would be interesting to see a worldwide distribition
wonderful,always smiling and enjoying teaching.the new approach to quadratic i missed in high school.keep up the good work and be blessed.kenians commenting.
Much Thanks Prof. Loh ... Outstanding!
Its just the quadratic formula
Very good alternative non-Guessing method for absolute Beginner. But for those exprienced people, they just look at the quadratic Ax＾2 + Bx + C = 0 , immediately write out the answer within split of second before the standard formula appearing inside their mind/brain ! This is human autoreflexive actuon through repeative practicals/failures . Action is faster than the Thinking mind. It is just like Chinese Primary School that everyone must memorised 9 x 9 or 12 x 12 multiply tables! after you left Prinary school and seldom use the multiplication tabkes for 10 yrs ,20 yrs ,50 yrs .Your mind already forget all the multiplications .But whenever somebody said A X B ! You immediately give the Result Faster than your mind thinking by Instingct ! I still prefer your alternative technique when teaching Beginners/Layman ! GOOD job keep it up .