You could factorize the second equation: x^4 (x - 3) + 3x^2 (x - 3) - 4 (x - 3) = (x - 3) (x^4 + 3x^2 - 4). You get one solution x = 3 and others will be 1, -1, 2i and -2i from the biquadratic equation taking x^2 = y and solve using shridharacharya formula. (x^2)^2 + 3(x^2) - 4 where x^2 = y so, it's y^2 + 3y - 4.
Thank you so much, I finally understand it. My teacher took 5 minutes to explain this and tbh I didn’t give her my full attention but she then told us to do the next 5 questions and we never even went over it so I was so confused. Not anymore 🤠🤠
Just wanna point out that this thing actually helped me in understanding the Rule of Signs. Although I'm really a good student in terms of maths, sometimes I go into roadblocks, and when I do, I refer to your channel to see where I missed. So far, you really had a good time explaining this! Thank you very much for this, and please continue doing the things that you love the most (helping other people understand maths)
While teaching the concept this week, my class and I found a neat shortcut for f(-x). Instead of evaluating the whole function, simply flip the sign of all the odd-powered terms!
I just wanted to thank you for the helpful tutorial you posted on Descartes rule of signs. I was struggling to understand the rule, but your tutorial made it really clear. I especially appreciate the way you explained the different cases and how to apply the rule.
You just saved me my pre calculus when nobody else (Especially not my workbook) explained it well My book basically just said, "Hey here's math there's probably a way to do it but we aren't going to tell you, go" you've earned a like
Nope because odd number changes the sign like -5*-5 = 25 but -5*-5*-5=-125 don't look at the numbers but the sign instead so odd exp change the sign and even exp don't change sign
You are helping to so much to review polynomials. I was thriving since I transported school and missed this chapter. I was finally going over them a week before the school starts and I feel like I mastered how to solve polynomials from all your videos. Thank you so so much. Also, maybe a video with conjugate root theorem might help more students cuz it's always together with these.
I know we are all thinking it, his Ss' are very sharp. To fix this you can add a "DeEsser" to your audio in a video editing program. Or you could get a popfilter for your microphone
Maybe tovmake sure that our roots our correct, for instance if we said first that we'll have for example 3 positive roots and two imaginary ones, and after solving we have (for example 4 postive roots) than we'll conclude we made a mistake
Descartes' rule of signs will narrow or lessen the number of choices of possible zeros when we are doing trial and error, by knowing how many negative , positive, or imaginary zeros that can be there, we will not waste our time finding more negative or positive zeros than how many it should be.
@@010.gutierrezdarylljamesd.7 Really? I don't see it that way at all. It should be pointed out that I'm also very retarded but i digress. If i see that there are 18 possible zeros, and use Descarte's rule to find out that out of those 18, 4 of them are either positive or imaginary, then i still have to shoot in the dark 18 positive numbers to narrow it down, which to me is incredibly tedious. Of course i won't literally have to try them all, and with intuition you can guess which ones it won't be, but still. I hate it. Is there really no other way except this foggy (though with a slightly clearer path) trial and error? Would figuring out a better way be a mathematical breakthrough or has it been figured out this is the only way? Or is a better solution taught later on but requires more difficult concepts?
@@ColombianThunder 18 possible rational zeros? 18 possible zeros period,? (which suggests an 18th degree polynomial) What degree polynomial function are you dealing with? Newton's Method of approximation of zeros may help eliminate some choices if your function is a polynomial (i.e does not oscillate uncontrollably). You learn that in Calc I.
Just feed the coefficients to a number crunching polynomial root finder softwate (like online Wolfram), and forget about Descartes Rule. Not to say that polynomial equations in real engineering are gonna look like: x^3 + 3.1567 x^2 - 0.198x + 45.934 = 0 No way for guesses with nice single digit integer numbers.
bruh my teacher literally just reads what's on the screen and i can't understand a thing now she wants us to answer it like we all understood what she said.
I understand the concept but at 3:55 he mention 1-2 and that there can't be negative sign changes. Clearly this make sense but I dont understand why he mentioned and what 1-2 even has to do with this situation?
Quick question : IXL taught me that you can add or subtract the amount of roots to get different amounts of roots For example, if you have a cubic function, that could have 1 negative zero, then you can say it also could have 3 negative 0’s
Mathematicians describe it like: (Descartes’ Rule of Sign). The number R of real roots of A(X ) in (0, ∞) is bounded by Var(A) and we have R ≡ Var(A) mod 2. Then Silvanus P. Thomson enters and says in the prologue of his magnificient book Calculus Made Easy this "The fools who write the textbooks of advanced mathematics - and they are mostly clever fools - seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way."
based from all of your examples all roots from negative are 1 what if its more than 1 like 3? How would you create the table? example: degree = 7 (+): 4, 2 0 (-): 3,1,0 ::: (+, -, i) does the possible combination follows a plain decreasing pattern? (4,3,0) (2,1,4) ? or nCr table? (4,3,0) (2,3,2) (0,3,4) (4,1,2) (2,1,4) (0,1,6) (4,0,3) (2,0,5) (0,0,7)
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great video
You could factorize the second equation: x^4 (x - 3) + 3x^2 (x - 3) - 4 (x - 3) = (x - 3) (x^4 + 3x^2 - 4). You get one solution x = 3 and others will be 1, -1, 2i and -2i from the biquadratic equation taking x^2 = y and solve using shridharacharya formula. (x^2)^2 + 3(x^2) - 4 where x^2 = y so, it's y^2 + 3y - 4.
honestly, i did not understand descartes rule of signs for my precalc class until this video... you explained it wayyyyy easier than so many others
I'd say he skipped some of the explanations but it's good
It's literally 2AM and I'm here... Finally understood this.... Unbelievable!
Can you begin to imagine what this cat scored on his SAT?
Thank you so much, I finally understand it. My teacher took 5 minutes to explain this and tbh I didn’t give her my full attention but she then told us to do the next 5 questions and we never even went over it so I was so confused. Not anymore 🤠🤠
Just wanna point out that this thing actually helped me in understanding the Rule of Signs. Although I'm really a good student in terms of maths, sometimes I go into roadblocks, and when I do, I refer to your channel to see where I missed. So far, you really had a good time explaining this! Thank you very much for this, and please continue doing the things that you love the most (helping other people understand maths)
Recently.... These tutorial videos are becoming my life savers🤍
Greatfull to you....
From Bangladesh
On 12:23 we can factor by grouping cuz the each two groups of therms are with the same coefficient's ratio.
this man just saved me from failing algebra 2. absolutely legendary
lol same
Thanks so much dude, you're like a legend among high school math students. Thanks so much for making this video. It literally helped so much. Thx!
Yo. You need a medal. Thank you 🙏
While teaching the concept this week, my class and I found a neat shortcut for f(-x). Instead of evaluating the whole function, simply flip the sign of all the odd-powered terms!
So many concepts in a single video wow your videos are awesome your a life saver thank you
I just wanted to thank you for the helpful tutorial you posted on Descartes rule of signs. I was struggling to understand the rule, but your tutorial made it really clear. I especially appreciate the way you explained the different cases and how to apply the rule.
That was complex on the first take. You moved slow and it made sense. Though practice is needed to let it all burn in. Thank you
Your were extremely thorough and your explanations were excellent!!
MR. Organic Chemistry Tutor, thank for an awesome introduction to Descartes Rule of Signs in old fashion precalculus.
Me watching this 20 mins before my exam starts: 👁👄👁
I feel you there
Got mine in bout 10 👁🫦👁
I'm about 5 hr before 🐸
I have about 4 hours before mine
3 hours 😂
You just saved me my pre calculus when nobody else (Especially not my workbook) explained it well
My book basically just said, "Hey here's math there's probably a way to do it but we aren't going to tell you, go"
you've earned a like
Bro you just helped me pass my Math 151 final, thank you my dude😊
My finals are tmrw you made everything clear for me I appreciate that thanks
When you realize this guy has *194+* precal classes alone
(silently hits subscribe)
there's 240 now
☹️
When you thought you already get it but then when the video is nearing to end my mind goes brzzttt😃
God bless you man, you teach so good. You saved me
Bro's teaching on Valentine's Day. What a legend.
This was the best explanation on TH-cam. Thank you.
Best explanation I have heard yet. Thank you
8:35 it's the other way around. Odd exp=no change whatever the sign of x, even exp=changes to positive if x is negative.
Nope because odd number changes the sign like -5*-5 = 25 but -5*-5*-5=-125 don't look at the numbers but the sign instead so odd exp change the sign and even exp don't change sign
🤝you are helping so many generations sir
You are helping to so much to review polynomials. I was thriving since I transported school and missed this chapter. I was finally going over them a week before the school starts and I feel like I mastered how to solve polynomials from all your videos. Thank you so so much. Also, maybe a video with conjugate root theorem might help more students cuz it's always together with these.
Thank you so much! I am in 6th grade and really needed this!
You were learning this in 6th grade I'm learning this in college and it's confusing for me
u taking algebra 2 in 6th grade? damn
@@uttkarshtewari2532 lol thanks! Now I'm in 7th and doing precalc
@@emilyjohnson2544 wow gl in high school
@@emilyjohnson2544 gawd damn i'm just learning this rn in 10th grade
These videos definitely come in clutch when you miss class
dude, you are like the jack of all trades!
Thank You very much. You have lessened my headache trying to understand this stuff.
Thank you so much. You're such an incredible narrator.
This just clears so much of my confusion thank man
When most of the comments are college students then me being a 10th grader here be like: * ._. *
lmao yuhhh, sophomore gang 😂
Same
Same
Ifkr I'm d y i n g
x_x brain hurt
It just clears so many confusions
thank you sir .God bless from Phillipines
amazing video ... thank you sooo much.... I have a test tomorrow and you literally saved me :)
this guy is better than my maths teacher wtf
you literally saved my life.
thanks for helping me complete my hw
I'm so happy this man won't let me fail 8th grade :D
You made it so clear!! The best!!
Bro thank you so much, I actually understand this stuff now.
This guy and Brian are carrying my Pre-Calc grade.
GREAT EXPLANATION! I FINALLY GET IT!
Thank you for breaking this down so easy ❤
You’re a legend
THANK YOU SO MUCH
Such great way to teach!! Hats off.
One way to avoid using synthetic division way is -
x^5 - 3x^4 + 3x^3 - 9x^2 - 4x + 12 = 0
x^4(x-3) + 3x^2(x-3) -4(x-3) = 0
(x-3)(x^4 + 3x^2 - 4) = 0
(x-3)(x^4 + 4x^2 - x^2 -4) = 0
(x-3)(x^2(x^2+4)-1(x^2+1)) = 0
(x-3)(x^2-1)(x^2+4) = 0
So x= 3,1,-1, 2i,-2i
So 2 positive ,1 negative, 2 imaginary
thank u sir ,you have saved me indeed.
I know we are all thinking it, his Ss' are very sharp. To fix this you can add a "DeEsser" to your audio in a video editing program. Or you could get a popfilter for your microphone
what is the utility of this rule if we actually have to find the roots ?
Maybe tovmake sure that our roots our correct, for instance if we said first that we'll have for example 3 positive roots and two imaginary ones, and after solving we have (for example 4 postive roots) than we'll conclude we made a mistake
To predict our answers and make sure the roots are correct
Descartes' rule of signs will narrow or lessen the number of choices of possible zeros when we are doing trial and error, by knowing how many negative , positive, or imaginary zeros that can be there, we will not waste our time finding more negative or positive zeros than how many it should be.
@@010.gutierrezdarylljamesd.7 Really? I don't see it that way at all. It should be pointed out that I'm also very retarded but i digress. If i see that there are 18 possible zeros, and use Descarte's rule to find out that out of those 18, 4 of them are either positive or imaginary, then i still have to shoot in the dark 18 positive numbers to narrow it down, which to me is incredibly tedious. Of course i won't literally have to try them all, and with intuition you can guess which ones it won't be, but still. I hate it. Is there really no other way except this foggy (though with a slightly clearer path) trial and error? Would figuring out a better way be a mathematical breakthrough or has it been figured out this is the only way? Or is a better solution taught later on but requires more difficult concepts?
@@ColombianThunder 18 possible rational zeros? 18 possible zeros period,? (which suggests an 18th degree polynomial) What degree polynomial function are you dealing with? Newton's Method of approximation of zeros may help eliminate some choices if your function is a polynomial (i.e does not oscillate uncontrollably). You learn that in Calc I.
Thank you! This helped me understand how to find imaginary zeros 😁
MY SAVIOR🙏🙏🙏🙏
😇
Made everything easy. Thank you!
Thank you
Just feed the coefficients to a number crunching polynomial root finder softwate (like online Wolfram), and forget about Descartes Rule. Not to say that polynomial equations in real engineering are gonna look like: x^3 + 3.1567 x^2 - 0.198x + 45.934 = 0
No way for guesses with nice single digit integer numbers.
props to this guy for actually explaining shit unlike my teacher
For the second example it is possible to factor by grouping because you could factor an (x-3) from each pair of terms
My college algebra professor sucks at teaching. So after our classes where I’m completely lost, I come onto TH-cam and learn using this guy’s videos🫠
Excellent Explanation sir. Thank you very much ...
This man deserves a free pass to heaven for the number students he saved from failing their classes.
Great video! Thank you!
Thank you! Great explaination
I'm just cramming before a math competition.
Well done...good pace...
Thanks so much ! Keep up your good work😊
You are a heaven sent.......YOu are a heaven sent.....an angel...
Thank you this lesson is very helpful
Very helpful. Thank you.
I love this guy his videos always help me all my classes .. in chemistry and math last year, and even physics (and math again) this year.🥹😁
This helped me so much!!!!!! Than You!!!!!
This video very helpful, thank you verry much.
i was so satisfied you fixed that line (7:16) that really relieve my OCD there thanks hehehe.....
You helped me a lot.thank you....
Love from india
tkssss so much, its helpful a lots
Thanks! your vids are so helpful
Thanks a lot dude!
bruh my teacher literally just reads what's on the screen and i can't understand a thing now she wants us to answer it like we all understood what she said.
I understand the concept but at 3:55 he mention 1-2 and that there can't be negative sign changes. Clearly this make sense but I dont understand why he mentioned and what 1-2 even has to do with this situation?
Thank you, soooo much!!!!
thank you so much!!
Quick question : IXL taught me that you can add or subtract the amount of roots to get different amounts of roots
For example, if you have a cubic function, that could have 1 negative zero, then you can say it also could have 3 negative 0’s
So in the first problem, didn’t you miss the case where there are 3 negative zero’s?
@@shangjiang3320you can only subtract by 2 and you cannot go below 0.
Thank you very much really pleased me
This is so helpful, thank you so much
Sup dude how you doing?
am i the only 9th grader here? it hurts my mind lmao but this video rlly helps!!!
Crystal clear
at 7:59 why you subtracting it by 2 ? can anyone tell me why
Thanks a lot! 💕
Mathematicians describe it like: (Descartes’ Rule of Sign). The number R of real roots of A(X ) in (0, ∞) is bounded by Var(A) and we have R ≡ Var(A) mod 2. Then Silvanus P. Thomson enters and says in the prologue of his magnificient book Calculus Made Easy this "The fools who write the textbooks of advanced mathematics - and they are mostly clever fools - seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way."
when its imaginary, the conjugate is also a root right? assuming all coefficients are real and rational
Lovely video
This is very helpful! Great explanation and organized. Thank you a bunch :))
based from all of your examples all roots from negative are 1 what if its more than 1 like 3? How would you create the table?
example: degree = 7
(+): 4, 2 0
(-): 3,1,0
::: (+, -, i)
does the possible combination follows a plain decreasing pattern?
(4,3,0)
(2,1,4) ?
or
nCr table?
(4,3,0)
(2,3,2)
(0,3,4)
(4,1,2)
(2,1,4)
(0,1,6)
(4,0,3)
(2,0,5)
(0,0,7)
loved it....