Vieta's formulas with examples

This video is about Vieta's formulas. I included a good variety of problems.
Send me a tweet at @SyberMath if you want to share a picture of your solution/ideas and comment here with the link to the tweet.
#NumberTheoryProblems #VietasFormulas

[ShortsOfSyber]

Check out the short on Vieta's Formulas:

[SyberMath]

Here is the long-awaited video on Vieta's formulas. Event though they are basic, they play an important role in problem solving at advanced levels and they are FUN to use!!! LET ME KNOW WHAT YOU THINK!!! 😍

[kaslircribs]

Very interesting! You are a great math professor!

[sattimama]

your videos are really good and so much learning for the students. I teach maths. I would recommend your videos to students.

[muhtasimfuadtarif]

You should get more attention...those were very helpful...

[shivamomvideo]

So nice....this is the real beauty of maths🤩🤩

[chrissekely]

From 7:11, p = q = 7/4 (because p + q = 7/2). An equation that relates p and q could also simply be p = 7/2 - q.

[ashishpradhan]

First of all, this is awesome man. Thankyou so much for this revision🥰🥰🥰😍😍. Secondly, I have a small question. Is there any other possible relation between p and q in example 2???

[stephomn]

This was perfect. Thank you. I am sharing with my students immediately 👌

[shmuelzehavi]

I have a remark regarding problem (5).
It's much easier to solve the cubic equation: x^3 - 9x^2 + 24x - 16 = 0

by factorizing of the cubic polynomial.
We can easily see that one of the solutions is: x=1, and therefore we can write:
x^2 - 9x^2 + 24x - 16 = (x-1) (x-4)^2 = 0
The roots of the cubic equation are: x_1 = 1; x_2 = x_3 = 4 and therefore:
√(x_1 ) + √(x_2 ) + √(x_3 ) = 5

[utuberaj]

Just superb. The last two equations involving sq root solutions and 5th power roots were too good.
Since this was all about VIETA's formula examples, can you tell us the wjole proof of this formula? We all are quite familiar about the relation between sum and product of roots for QUADRATIC case that is quite easy to derive (by the way I did not know this was due to this great guy Vieta!). How is it derived for higher degree polynomial equations?
Look forward to a good one from Sybermath soon.

[golddddus]

x1+x2+x3=1; x1^2 + x2^2 + x3^2 = 2; x1^3 + x2^3 + x3^3 = 3
Using Vieta's formulas find x1^(-1) + x2^(-1) + x3^(-1) and x1^(-2) + x2^(-2) + x3^(-2)

[yogamulyadi]

Thanks for posting something so educated.,
I'm sure there will be so much people get enlightenment if you make something like this,
And maybe will be more valuable if you make list about this...
🙏🙏🙏🙏🙏
.
And, can you explain about Lucas Number next please...😁😁
🙏🙏🙏🙏🙏🙏🙏

[omarbektemir]

Hi, i have a question on 26:35 minute of the lesson, could you please explain why B is equal to zero, since actually it is equal to 4.

[scottleung]

Cool problems - I had a lot of fun watching you solve them! However, I have a couple of questions: 1) are Vieta's formulas only useful for quadratic or cubic polynomials, and 2) can you use them to find the roots of those polynomials if you don't already know them yet? I'm not sure if that last one makes any sense, but I remember one problem you did in which we were given roots a, b, c and we found possible solutions for them explicitly.

[papiyabasu]

Thanks a lot for this, liked and subbed.

[Napoleon]

How is "b" 0 on the 6th problem I don't understand

[elkincampos]

6 is not solvable indeed its Galois group is S_5 why?. Is irredutible because is a Eisenstein Polynomial for p=2 and the Discriminant is -2^4*p where p is prime. By theory of inertia group we can proof that Galois group is S_5.( The inertia group for p is a transposition, by S_5 is generated by a transposition and 5 cycle( f is irredutible).

[lakshya]

We study this in primary school in india 😜