life changing quadratic formula
ฝัง
- เผยแพร่เมื่อ 28 ก.ย. 2024
- There are different ways of solving a quadratic equation, such as by factoring, completing the square, or using the algebra 2 quadratic formula. But after watching this video, you will never use the quadratic formula ever again!
This method is pioneered by Prof. Po-Shen Loh at Carnegie Mellon University and has been invented by the Babylonians, but somehow forgotten with time. Enjoy this wonderful adventure into the wonders of mathematics.
Po-Shen Loh's webpage: www.math.cmu.e...
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During a math class, I accidently derived this method from scratch, I thought that this is a new method that no one knew, then realised this is the derivation of the quadratic formula that we were just not taught.
Same bro!
@@epc0003 it's quite possible
Sometimes you just don't wanna go with the said method and try your best to find another way to achieve the answer
One does not need to be Po- Shen Lo to come up with this
I also derived the formula during my class and showed to my teacher but he said " the book does not say so and I'll deduct your marks if u use the".... nvm I am so happy now that I was correct
@@epc0003 fr, it's really hard to derive this method from scratch as a student, how would someone come up with taking the midpoint of roots then using it as being equidistant from roots and calculating that distance to calculate roots, I always wondered why addition of roots and multiplication of roots was so easy compared to the quadratic formula but I would never imagine myself deriving this
@@vanshkhatri8233 lmao, this actually happened with me.
“Modern Problems Require Ancient Methods”
a wonderful concept.
Absolutely right
E C 100%
Ironic but sometimes true
Haha ancient chisel go brrr
When you simplify all the steps taken, it turns out that the _u_ is actually equal to √∆/2a, so this is quadratic formula but in multiple steps instead of single equation.
I just came to the same conclusion. This method basically derives the quadratic formula from "graphical" solution. Which I think, is actually quite educational.
My mathteacher used this “method”, well it’s actually common sense if you think it through, to explain us the abc formula
Yes of course. It’s not going to miraculously break away. But it is definitely an easier way to conceptualize the process. Most students just memorize the quadratic function instead of deriving it. Whereas this method fits nicely into the same method applied to whole number roots. Every student I’ve taught who just memorized formulas deprived themselves of seeing all the connections in math and as a result never become really good at math.
Perspective changed
@@johnspence8141 isn't the easiest way to just complete the square?
Can relate the formula for roots more intuitively now.
MID = -b/2a
U= sqrt(b^2 - 4ac)/2a
X1 = MID + U
X2 = MID - U
Thanks for sharing this.
Hey, thanks for compiling this!!
thanks for comenting us ew
Ah!
My math teacher is here too
My inspiration is here too!!!!
Hii
Legend
L e g e n d
Peyam you kept me interested in math! You were my gsi for math 54 back at Berkeley. Since then I didn't continue past abstract algebra but I still love math and I love this channel!
Ooooooh I remember you!!! Hope all is well 😁
Its all fun and games until the roots are imaginary.
Lol
do watch the video till end..he took that too!
@Guitarzen oh no😭
Make sure you are solving real problems
Make sure you watch the video before you comment? Complex numbers change nothing
Math Teacher: You weren't supposed to do that!
Grrrrr
All things aside, Dr.Peyam seems to be so good of heart. He seems to be a sweet,simple and composed person 💙....
People like him change the bad inside of a person and fill them with positivity 😎💞
My thoughts exactly 😀
What?
As russians we were taught this in like 5th grade. We call this формула Виета (Vieta's formulas), as they exist not only for quadratic equations
UPD: yes, you can use them for cubic too
oh so you can use them for cubic?
@@mathadventuress yupp
@@mathadventuress The formula states that for any equation of degree N which has roots A_i where i={1,2,3...} the sum of the roots is the coefficient of the term which has N-1 as power divided by the coefficient of the term which has Nth power TIMES -1... and just like this when the roots are taken two at a time and multiplied and then added like a series (to clear things up e.g (A1*A2)+(A2*A3)+(A3*A4)+....+(A_N-1 *A_N) )IS JUST THE THIRD COEFFICIENT divided by the the first one and and like so on I would suggest you to look it up on some good book like Hall and knight
Vietas formulas should be a must learn for polynomials of any degree. Sad it is not taught to many before university (not even a glimpse).
I learned it in 6th grade, and my teacher use to say if you want to learn math or science learn from Russian and one of my professor (one of the smartest person i met in my life yet)here is US proved it.
If **Dr. Peyam** says that he’s the nicest guy he ever met, that’s really saying something!!!
Truly!
yes, because probably the professor taught him something new.
Gay??
@@aryamannsrivastava7279
no!...we cnnot juge like every nice person is gay thats very wrong...instead in general poeple with a higher education like him are nice bc their are not in the level of juck kids who are looking for trouble or bulliying instead of mind themselves.
@@abderzakchebbi1339 I am sorry for my words .actually I myself found sir to be very useful and informative
Imagine someone considering this a scientific breakthrough and u applied it on high-school maths on a daily basis
Lol
True😂
You are a unacademian?
Ashwani Tyagi's students right?
search up po shen loh. He does a lot more real mathematics research (in graph theory and combinatorics) as a professor at carnegie mellon, as well as coach the usa IMO team. this is hardly a breakthrough or a new method in any means. not sure why he's calling it that.
You're an incredible maths teacher and a human. We need more people like you sir. You're so cheerful. You earned a subscriber here...keep uploading interesting mathematics stuffs here...love your content. I'm gonna use this method for quick solving in MCQs. Lot's of love and respect from the world.
Thankyou very much for this valuable information.
Actually after watching Prof. Loh's video, I tried to solve one problem myself. I used an odd coeff in the middle term to have fraction solving and to my amazement, it works! Now, I am excited to teach this to my students! :)
Wonderful!!! :)
WOOOOOWWW!! My highschool teacher taught me a slightly different variant of this method that was harder to understand back then. This video is very clear, very useful and well done. Great job!
I call this "completing the square" in a fancy way
🙂🙂🤣🤣
The equations at the beginning are called Vieta's formulas
I call it "Bhaskara formula with geometrical intuition" hahaha Completing the square is my go-to though
completing the square doesn't use symmetry in the same way. This is slightly different.
Yes, this is essentially finding a turning point and completing the square.
"Y'all already didn't know that?"
- This comment was made by Asian Gang
It is also standard, I believe, in most of Eastern Europe.
This was so basic... I didn't know this method had a name. We were taught this before quadratic formula.
Being an asian indian I didn't know this method, although I know some different easy methods to solve this equation. Always happy to learn more.🥰
Meet any CAT or CGL aspirent of india
I m from Russia and we use this formula and name of this “ the theorem of Viet” (Теорема Виета)😂😂😂
I like the fact that you explicitly wrote the implicit explanation for why Po-Shen Loh's method (yeah I just watched his vid beforehand) works. However I have one question, shouldn't this equation be equally valid if you use (x+x1)(X+x2) instead of (x-x1)(X-x2)...that way you won't have to keep changing the sign of the second term in the original equation e.g. in the equation at 2:08 the midpoint will be -3 instead of 3. I know you will have to change the sign of x1 and x2 to eventually get the roots though when using the form (x+x1)(X+x2), which is likely why you are using the form (x-x1)(X-x2).
TY, I cam to the same conclusion how can the sum of the roots be < 0 yet they are both positive.
If every teacher in Austria's art school back then was as cheerful as you, the world might potentially be a better place.
Lol
This is a very specific joke, i am surprised people got this
Ever heard of being cheerfully refused admission?
Is this a Hitler joke? Just want to make sure I’m right
@@brittonporter5063 yes
If every math teacher was as cheerful as you, everyone would understand math!
Cheerfulness has very little influence on understanding math...
@@tmjcbs it makes your audience be more interested, hence they will be more focussed and they will learn a lot more
I didn’t understand shit from this vid
@@tmjcbs No
@Nawfal. wns excuses. enthusiasm of the teacher doesnt matter. the actual content is more important. if enthusiasm has an effect on a student then thats just because that student is lazy and doesnt want to do the hard work part on their own.
It's Vieta formula's extension. They taught it in schools in USSR.
Minchia in Russia siete fortissimi
In russia too
well in india too.. we are taught vieta formula..
x^2 - (sum of roots) x + (product of roots)
@@infinixgaming1791
it's a bit different.
i learned that 3 years ago, but the loh's method use de discriminant for quadratic equations in a ''indirect'' form
the ∆=b^2-4ac is equal to u.
since there are many equations that cannot use x^2-sum+product.
This guy just seems so happy teaching ❤️ This can really change a lecture for the better
I've never seen a man this excited over teaching, congrats :D
Bro this is literally what's taught in Asian schools. I never thought this formula would change my life lol
american educatio system bro
i studied this in 7th grade morocco btw
@@hamzamoussaid8895 yep american system too boring, long and dumb
@@asal2667 bro, then why almost every best university in the world is in U.S?????
@@dmitricherleto8234 university and college maybe...but K-12 hell no
@@dmitricherleto8234 on what basis do you call it the best? just because they say so?
Pretty sure this *is* the quadratic formula, just with a factored out.
That is correct. In fact, he SAYS that if a isn't 1, you have to factor it out first. If you factor a quadratic using this method, and then using the quadratic formula, you find yourself doing all the same arithmetic. The difference is that if you are good at remembering sequences of operations, this will seem easier, while if you are better at remembering formulas, the quadratic formula will seem easier. They all break down to different rearrangements of the prototypical quadratic, ax^2 + bx + c = 0, to solve for x.
Lmao yea it is
To be fair, it will all be algebraically equivalent no matter what you do. This is just a different way of thinking about it. The equation becomes:
for a=1, x=(-b)/2 ± √[ (b/2)^2 - c ]
Honestly, this would be an easier way of evaluating the quantity underneath the root if b is divisible by 2. But, most importantly, it gives a better conceptual understanding which can save you if you forget the quadratic equation.
Thought so too!
when we complete the square its the same... the turning point -b/2a x-coordinate is the midpoint of the root ... the rest follows
i was taught almost this method in 1965.
rearrange the original equation as x² +2hx +d.
then x= -h +/-√(h² - d)
This is correct, but I'd like to point out that you would get the quadratic equation once you're rearranged the original equation to factor out the x^2 coefficient. So you end up doing exactly the same arithmetic either way, but the method you are showing splits it into two steps. What makes the quadratic equation nice is that once you have it memorized, it's just one step. So really it's a matter of whether you want to remember one equation, or a slightly simpler equation and another step. What I like about the method shown in the video is that you don't have to memorize anything, and even if you forget the exact process, it takes only a minute to go through the same derivation the describes.
I'm pretty sure I was taught a formula as x^2 +2ab + b
@@-ClerzZ- I'm pretty sure you weren't, because that would not have given you the correct answers. In fact, it doesn't even solve for x.
I agree. This video really does not add anything new to the solution of the famous equation.
But how could it? Everything here is completely known for centuries.
@@sasoblazic It gives students another option. The math is what it is. Whether you are plugging a, b, and c into the quadratic equation, or you're factoring by completing the square, or you're using this method, the actual arithmetic you are doing is identical. But different people remember things in different ways, so for someone who has no trouble remembering complicated equations, the quadratic equation may be the best way, while for people for whom remembering the steps in a process is easier, then this method or completing the square may be easier. You are right: this method that David Seed describes doesn't add anything to the mathematics, because just as what is described in the video is actually one derivation of the quadratic equation, and completing the squares is another, this is just preparing your polynomial a bit before crunching the coefficients through a simplified version of the quadratic equation. But for every student, ONE of these methods will click better in their mind.
There are also cases, though, that are easier to do with one method than another. For example, if the x^2 coefficient is 1, David Seed's formula is slightly easier to use than the more general quadratic equation, and if your coefficients are all integers, completing the square or the method in the video may be easier to apply.
For example, the solution of x^2.01-5x+6=0 is x = ((-5/1.01)Wq((-1.01/5)*((6/5)^1.01)))^(1/1.01) = 2.0302 (up to 4 digits). Wq(z) is the Lambert-Tsallis function and, for this case, the parameter q has the value q = 1-1/1.01.
Everyone:Using this method
Me: nEgaTiVe Beeeeeeee pLus oR mInuS tHe SqUaRe rOoT oF....
FFFFFFFFFFF
It also tells you if the roots are real or not. For me its a lot quicker to solve using that formula. The only problem is remembering it by heart.
Omg now I have that song stuck in my head again 🤦🤣
@@Fakipo join the cult
th-cam.com/video/E2eVZFy9yzk/w-d-xo.html
@@bonnieb7608 yes
Following along with this made me realize where the rule
"If a polynomial has integer roots, they evenly divide the constant term of the polynomial" comes from
because if you expand (x - x1)(x - x2)(x - x3)... the last/constant term will always be x1*x2*x3*...
I was always just told, "if you want to guess integer roots, guess all the factors of the constant term" and never questioned it.
yay, learning
Yeah. This lets you guess the roots when they are integers. Which is fine for passing math tests, but doesn't come up so much in the real world.
Teacher : This is the simplest method.
Middle term factor : "I don't even exist"
Westerners be like: that's cheating😭😭
x^2 - 9 = 0 : idk😂😂
The name of the formula is middle term factor, so by its name you have to factories the middle term coefficient of the given equation by the help of initial and terminal terms.
Here( -6) is the middle term coefficient and -6 = (-4)+(-2) . ( where { -4}×{ -2}= 8).
So the Answer will be (x-4) (x-2).
@@LLT_MATHEMATICAL_FLUID kehna kya chahte ho??
@@adityagarg9988 x=+-3
Everybody learns this formula in school in Germany. It's called Vieta's Formula or p-q-Formula (the general solution formula).
also in Italy, it is considered the basis of second degree equations, you learn in the first grade
Also in Russia, it is one of the basic formulas
Never studied it as a part of curriculum in India
@@pizzamidhead2183 I knew Italians were smart, but how do you teach quadratics to 6 year olds. That’s crazy
@@yagnapatel3912 Probably first-grade high school students.
Legend: Uses the quadratic formula.
Ultra Legend: Uses this method.
Me: I use my calculator.
West Bengal naki Bangladesh????
INDIA te to calculator allow kore na wbjee &jee main etc te!
@@amitavadass maybe he's in a college
@@DANTE-kv7mv hoyto!
@@amitavadass Bangladesh eo korena dada
@@amitavadass jee 2021 or 2022
Love the fact that this got recommended to me when I’m about to have my exam in 2 weeks 😀
I too.
Careful, in exams it can be equally important that you're examiner recognises you go a "working" way to the solution. Then, if you make a mistake they may give you marks for the way to the solution.
(Still, I agree it's a wonderful way, especially because it always goes with understanding of how the solution works.)
How did it go?
@@KayOScode it was extremely easy actually
@@mayaghazy391 I love it when theyre easy. Hoping my compilers midterm is easy this Wednesday lol
in russia, Vieta's theorem is taught in grade 8, so I don't understand your delight :D
P.s. srr for bad eng, its google translate :3
He's from West
In China, the method was taught in grade 7... But it’s a great method, anyway.
Here in Czechia, it's taught in 6 grade, maybe even in kindergarten we spoke about it among boys... (Just joking, I am not from Czechia)
@@hanzhoutang9235 Chinese people are machines! They work alot to use their full potential. I am a 10 grader and learnt it for the very first time
I thank TH-cam algorithm for showing me this videos in my recommendation. And thank you sir.
Lmaooo
Me looking at the title, "I bet this has something to do with viete's theorem" sure enough it does! Just learned about this in class this semester
Only took me 32 years of my life to stop using the quadratic formula. TY.
I know what I'll be teaching my kids when they are studying quadratics in school!
If they're more visual math learners, like me, they might prefer to Complete The Square, using an area model (the same thing).
No, don’t do that. They are taught the formula for a reason, most questions will require the formula, you get marks for working, if you do that you will confuse them and they will lose marks
My life changed after watching this video, now I drive a lambo and live in a castle. Thanx dude.
im in Calculus BC in my senior year of high school in the United States and I've never been taught this!! so cool
So are you saying that people didn't know this? Like before learning the quadratic formula?
Yes.. in NCERT its done before doing quadratic formula.😂in 10th
@@sarbjeetsingh9137 I know but nobody uses, all do these questions with the splitting the middle term
Tho these identities were told in class 9
@@lime-limelight that's true what you said tanish
Just apply Shri Dharacharya's quadratic formula 😄 it'll save your time.
don't think western guys are that good at maths ...i saw another video where goras were surprised seeing Indians telling squares and square roots of natural numbers .
This is basically depressing a polynomial no?
This is related to an important step in solving the general cubic equation.
Yes it is.
That’s harsh, we should be nice to the polynomial to help it overcome its depressive roots
Depressing a quadratic is equivalent to "completing the square".
Huh! This kind of methords are everyday used in class 11 problems for IIT JEE
Proud to be jee aspirant 😊
Yes🤣.. in india 10th ka bachha ye kr lega😆
Mein to ye 6 class mein sikh liya tha
😂😂
It's so smart! Why is it not taught everywhere?!
Because it actually IS taught. It is based on completing the square, which is a method used in deriving the standard quadratic formula. If you recall its derivation, you can clearly see how they are identical.
@@fullfungo Yes, I know that this is how the Greeks worked it out as well, but schools just sit down you in front of the equation.
@@fullfungo then why is he touting it's different if it's the same?
@@Icenri They do? I don't recall that ever happening for me. Maybe it's just some places where it's taught worse?
@@leif1075 Having different methods to obtain the same result may seem pointless. However, some of them may be more intuitive for a human, while others are more efficient for a computer. There are of course other reasons, but these two are usually the ones that help us make the choice when presented with one.
This is just the quadratic formula done as an algorithm. Very nice
yup more exactly the variation of the quadratic used in Germany and India. The Pq-formula. (way less of a headache than the American formula and all you really do is divide by a)
@@Metalhammer1993 Yeah, can belive so. remaber when I first learned the formula, was a headice to memorice
@@alakas706 the american one really is a monster. the PQ one is a bit simpler
My God, the rest of the world uses the ABC formula? I hate that monster.
@@m.m.2341 yup. I at least only know Germany and India
I’m a half century, first time in my freaking life I see this method, I was always taught to “use your instincts’ basically instead of the midpoint and the minus sign before the second term of the equation.
Well, I thunk that after 25 years of obtaining my university degree, my certified professional title and 27 years of labor experience (yes, I started working on my career two years prior to license and degree), it’s never too late to learn something.
Sri dhracharya rule to find roots of quadratic equation is way better and easy...
Yes Sridhar Acharya's method is more easier.
Yes.
They are fools😅
@ayo tebak siapa and why u feeling jealous by this?
This is true...evan u also use this method
I thought we just have to find pair of factors of the c, and if that pair's sum is the value of the b, then those are roots (in ax²+bx+c). Isn't this simplified factor method easier than the video? We can even calculate using this mentally on our 7th
In general if the roots are irrational, then no
Rolan Samonte this kind of vidoes could save you much time looking for the correct answers
For irrational roots, it's hard, it may take time.. It's possible but it ain't easy.
This method is derived from Sridhar Acharya formula sum of roots -b/a and product of root is c/a in quadratic ax²+bx+c
It’s the other way around, your formula follows from this method
The pq-formel one learns in germany is basically the same just put into one formula. Always am perplexed that quadratic formula is used in america
it's too hard to teach students to divide by leading coefficient.
I would assume that it is because the pq-formula is the solution to the equation x^2 + px + q = 0, while the quadratic formula instead solves ax^2 + bx + c = 0, meaning that, it is originally intuitively easier to understand the application of the quadratic formula, since it practically works for all quadratic equations, while the pq-formula occasionally requires simplification of the equation to fit the standard form.
Teaching US students a simplified method would lead to a LOT of confusion when dealing with more complex quadratic equations. I've seen a lot of different methods taught by teachers and the confusion isn't diminished among students, so I don't think it's the method that's the problem.
@@GaussianEntity if anything its the number of different methods that confuses students
People in this country are actually presented with either of both formulae.
We have learned much much easier method insolving these equations in India. Now our pride in our education system increased manifold after viewing this video.
Seems sus why Dr . Peyam didn't heart ur comment altough he hearts everyone's comments
On the other hand, the general analytical solution of a^x + b^x = c^x can be found in "On the Solutions of a^x + b^x = c^x" that can be download on Researchgate too.
Thank you sir! Very insightful, makes me want to play with maths with a different perspective....wow truly eye opening
"Change my life" is a bit far of a sketch but, still interesting.
I never thought that there might be different ways to do maths.
Learning maths like a religion seems wrong. Learning anything like a religion seems wrong.
This sparked my curiousity to find simpler ways to solve problems, rather than following the herd.
Ofcourse understanding the fundamentals is necessary, but sometimes teachers make things so complicated for no reason.
Nevertheless, this was helpful in a way and therefore, I am grateful.
It's very interesting how this method that Professor Po Shen Loh has popularized in his framework is midpoint centric whereas the completing the square method to get the quadratic formula is very area centric. The 2nd paradigm hails back all the way from Al Khwarizmi's time as you say - I'll take your word midpoint paradigm existed since ancient Babylon as well it's just its going through a weird resurgence in popularity, 1st back when it was conceived, 2nd when Francois Viete and other French mathematicians looked at sum and product of roots of polynomials, and now today with Po Shen Loh and you Dr Peyam.
i wish my math teachers were as cheerful as he, i would have learn math.
I think your English teacher was also not cheerful
😂
@@dragster9474 🤣🤣
@Aadi Ringay which method?
I'm pretty sure u would be making fun of him
2:40 just put x1 = 8/x2 in upper equation you will directly get the answer
this generalizes into the quadratic formula
I was curious, so I did the work using A,B and C for the coefficients and was not surprised that they quadratic came out. I guess some people do better memorizing a formula, and others do better memorizing a method. I'll stick to the quadratic.
@@FrankTuesday And madmen compute the quadratic formula from the general form of the quadratic equation in the middle of the test.
yes but this can be used for higher order polynomials
@@bobross5716 how?
@@martin-__- just add more terms when you initially factor out the equation e.g. (x-x1)(x-x2)(x-x3)... and continue the process from there.
Thank you for sharing this easily understood and accessible method of determining the roots or a quadratic. I always disliked memorizing something if I couldn't derive it and if, instead of using numerical coefficients, I use this method on ax^2 +bx +c = 0 the "Quadratic Equation" I had to memorize just falls out. (As it should!) Thank you.
Thanks so much!
1 year on and Dr.Peyam is still giving hearts
Am I the only one that thinks the mid-point diagrams with the two "U"s over them look like cats?
Now I can't unsee it.
UwU
Good catch. Yes they do.
No, but that, combined with the two 'U's over it led me to wonder if it was going to end up being a drawing of a dog's face, or something.
You had me at "You will never use the quadratic formula ever again" 🙌
Engineers: "just type it into Matlab!"
@Fahad Zafar its language to represent to Visualise data
@@rudrasama297 "to represent to visualise data"
Godzilla had a heart attack reading this
@@robinsingh9102 is he Dead now? Or you transplanted your heart?
I independently discovered it myself, too, when I was in highschool! I call it "The MD Method". It has three steps:
1. M= -b/2a
2. D= (M²-c/a)^½
3. x= M±D
Hope this helps. After some more scribbling, I found out that it's basically just quadratic equation torn apart. LOL.
Everyone learns this if you do A level further maths, it’s a topic called roots of polynomials
Ah yes, a fellow further mathematician
@@Stxrmz well hello there. AQA?
@@harrygraham9690 Edexcel
I read it during JEE prep
this way can be written as x=m+-sqrt(m^2-d) where m is the midpoint for the normalized equation and d is the constant term of the normalized equation. we can easily achieve the quadratic formula from this: we have ax^2+bx+c and then we normalize to get the scaled equation x^2+(b/a)x+c/a which has the same roots
here we see m=-b/2a and d=c/a
plugging in these values into the formula above will give you the quadratic formula after some simplification
the reason it was 'tarnished' with the quadratic formula: look at the quadratic formula with a=1. x = -b/2 ± sqrt( (b/2)^2 - c); this is exactly the formula you presented: the midpoint is -b/2, and from this midpoint m, you get (m-u)(m+u) = m^2-u^2 = c, then u = sqrt(m^2-c), and x = m±u, hence -b/2 ± sqrt( (b/2)^2 - c)
Ah yes, I lost track while reading but this seems right
Yup agree 👁️👄👁️
Back in 1980s when I was in junior high, one of my math teachers in
China taught us below formula to solve any quadratic equations ax^2 + bx
+ c = 0, then we have (-b/(2a) - u)(-b/(2a) + u) = c/a, then we have (u
+ b/(2a))(u - b/(2a)) = -c/a. Solve the u we will get x = -b/(2a) - u
or x = -b/(2a) + u.
Awesooooooooomeeeeeee
Why did someone not taught me this in my childhoood.
That honestly reminds me alot of the p-q-Formular wivh is a simplified version of the quadratic formula.
at the end it is the same as the pq-formula.. the midpoint is - p/2 and then plus/minus u and u is the square root of the discriminant. It is just a nice interpretation.
5:16 - it's a Nightmare 😅😅
With a certain amount of practice.. the roots can easily be found on mind command.. for complex roots I prefer using the Shri dharacharya jis formula .. which is a lot simpler...
What he did is same thing essentially
Other way would be substitution, I find it as an easier option for solving higher order polynomials than their formulas. Dr. Peyam, can you please show if there is any similar way to solve higher order polynomials like the one you showed in this video.
It already changed my life in the first 30 seconds.
I have seen basically this method before on you tube where they start with the fact that the coefficient of the x term is the negative sum of the roots and the constant is the product of the roots . I did like your presentation though . The way you show how easy it is to find the mean and the difference to subtract and add leads to an effortless algorithm to find the roots .
an even more simpler way is to Differentiate to equation. then the value of x can be found easily and quickly
It doesn’t work in every equation tho. And you only find one root
Need a math and physics teacher as excited as you are
We use this concept in 10th grade textbook 😎😎.
How much grades do you have?
You can use the simplest formula for quadratic eq given by Shree Dharacharya(Indian)-
X= (-b+-√b^2-4*a*c)/2*a
If the eq is in the form of ax^2+bx+c=0
you had to post this after i had a test on quadratics huh
Lol rip
@@vivek-zo2yy Thank you sir for your confirmation
@@evelocz :[
@@prodbyrish lol
this is literally just the pq-formula if you put every step in once
No its sacred ancient knowledge!
Wanted to write the same.
For finding midpoint you can say
In
ax^2+bx+c = 0
The midpoint is - b/2a
& for product It's c/a
It works absolutely
You can even draw this equation easily
See? We found the roots without any required efforts! 😅
A good question is: What are the analytical solutions if the equation was ax^2.1+bx+c, for example? The general solutions of the equation ax^r+bx^s+c = 0 can be found here "Solving the Fractional Polynomial ax^r +bx^s +c = 0 Using the Lambert-Tsallis Wq Function" that can be downloaded on Reserachgate.
This is so much helpful even for entrances , thank you
Please make more such videos on other daily maths problems!!
This is basically the quadratic formula for even-b's through a graphical understanding, it doesn't make solving the roots faster than the even-b quadratic formula
We had learnt it in middle class..
Even geometric representation of quadratic gives this type of conditions of Roots.
yeah
THIS IS ABSOLUTELY WORKING ! KEEP UP THE GOOD WORK
This is known as "middle term splitting" in India. We are taught this in 8th grade
but you can't use splitting the middle term in these 5:13 kind of questions, obviously everyone knows splitting the middle term and this approach towards finding the root is different
Bruh, 8th grade 😯, I'm taught this in grade 10
@@aatifshaikh9786 multiply the expression by 9 to obtain a simpler and equivalent expression and then split the middle term.
@@achintyajai2934 you are right. my older reply was poorly phrased. What i was trying to say was that his method is not splitting the middle term, it is different.You are correct by the way.
It's just a parameter change. What you show here is that using this approach for this particular quad equation that you can solve for real roots perhaps as fast or a little faster.
Point 1: The amount of work is no longer or shorter in general compared to traditional quad formula. This depends on your equation. Point 2:With this method you lose the intuitive nature of the Quad Formula. At a glance a person who has learned Quad formula can get the center info exactly the same as one does with this method. The rest of quad formula is just the distance on either side of this center. Where the quad formula is better though is that one can tell at a glance if the relationship has real or complex roots and finally how many of each.
Try this equation, 10x^2 +2x+1= 0 and race someone who uses quad formula to answer. First tell me, will you have one real, two real, or complex roots before you calculate the center (use only the knowledge of your method). A quad formula user can do this in seconds. Anyone can write a quad equation in such a way that it slightly benefits one method of calculation over another. That does not mean that some method using an arbitrary parameter change is necessarily a better method overall. I am sure someone could show you a different parameter change then cherry pick a good quad equation to solve quickly with it. IMO, this method falls far short of the value of quad formula since you lose all intuitive info indirectly supplied by quad formula.
When we teach, we should first gain a deep understanding of our material. I don't think this method is anything new. I believe it was how the ancient Sumerians and then Babylonians solved in a similar fashion.
I can confirm that this is life changing
It's takes time!!! I will soon upload the best way to find zeros of quadratic equations in one step!!!
10/10 for ingenuity and 0/10 for practicality... It is a NO from me...next
Yeah The Quadratic Formula is still the best way to get the solution quickly and besides this method (one being explained in the video) is really just deriving the Quadratic Formula in an indirect way.
Eh, I'd say it's probably more practical for the geometrically inclined. It's probably a net loss of time in terms of steps but maybe some crazy mental calculations can shave a lot of those steps to make it worthwhile.
I read this in my school in 9th class. and now I am in 11th and still in India we are using this method for solving quadratic equations and many other problems.❤️❤️
Achi bat hai
So productive channel it is. I've just found it today. This method is indeed good. Although, if I fail to do “splitting of the middle term” I use “-b+-[b2-4ac]^[1/2] /2a” which has become fast for me as I have learnt the squares for exams. We have several exams here in India for recruitment in Government Authorities in which Mathematics plays a vital role. It's inevitable and I love it.
Hindhu Shridhar Acharya. But sad part is it is not mentioned in our textbooks. I found it from other reference books.
I mean this is great and everything but I found the roots in 15 seconds by just guessing and checking🤣
I got the answers in just a glimpse of 1 sec
Saved me all kinds of times on tests. Comes from being raised by my grandfather and old math.
Sometimes it can be harder the factorise or complete the square, so this method could be useful in those situations. Such as when the coefficients are fractions.
That's because he intentionally used easy examples to explain the process - which also helps as we can see that it comes out the same at the end.
The underlying issue here is that a parabola has a vertical axis of symmetry which runs though the midpoint between the roots. In the country I am in kids are taught to use this fact to be able to find the min/max of a quadratic without using calculus.
If you know where the quadratic formula comes from, then this „method“ should be nothing new.
This is a bit of modern confusion!I actually mean that if we equate that further by substituting U there,we actually get back tye quadratic equation!You can try it!But still a good job in understanding the equation easily!
x= (-b/2a) ± U
x1= (-b/2a) + U
x2= (-b/2a) - U
x1 * x2 = (c/a)
(-b/2a)^2 - U^2 = c/a
or,U= √((b^2)/4(a^2) - c/a)
U=√(((b^2)-4ac)/4(a^2)). By LCM
U={√((b^2)-4ac)}/2a. Square root of 4(a^2) is 2a
x=(-b/2a) ± U
x=(-b/2a) ± {√((b^2)-4ac)}/2a = (-b±√((b^2)-4ac))/2a (common denominator) quadratic formula
I hope I have explained you!Thanks
Good for you
This is how American math teachers mess up serious teaching and learning process.