MHB What are Vieta's Formulas in Polynomial Functions?

AI Thread Summary
Vieta's formulas relate the roots of a polynomial to its coefficients, providing a method to derive relationships without finding the roots directly. The discussion highlights three approaches to solving a polynomial problem: checking roots, applying Vieta's formulas, or expanding a specific polynomial expression. Participants express uncertainty about Vieta's formulas and seek clarification on their application. The conversation reflects a mix of problem-solving strategies and a need for deeper understanding of polynomial relationships. Overall, Vieta's formulas are emphasized as a valuable tool in polynomial analysis.
mathland
Messages
33
Reaction score
0
I say the answer is A.

FB_IMG_1611815549152.jpg
 
Mathematics news on Phys.org
Did you check it? Did the roots come out? (They don't.)

There are three ways to do this one.
1) Cheat and find the roots of all your possible answers.

2) Use the Vieta formulas.

3) Write out [math](x - 1) \left ( x - \dfrac{1}{ \alpha } \right ) = 0[/math] and expand.

-Dan
 
topsquark said:
Did you check it? Did the roots come out? (They don't.)

There are three ways to do this one.
1) Cheat and find the roots of all your possible answers.

2) Use the Vieta formulas.

3) Write out [math](x - 1) \left ( x - \dfrac{1}{ \alpha } \right ) = 0[/math] and expand.

-Dan

No. I did not check it. What is the Vieta formulas?
 
Beer soaked ramblings follow.
mathland said:
No. I did not check it. What is the Vieta formulas?
Translation: I don't know man. That sounds like a lot of work!
 
mathland said:
No. I did not check it. What is the Vieta formulas?

Vieta's formulas are equations that connect some expressions of the roots of a polynomial equation to its coefficients. (See e.g. wikipedia)
 
Theia said:
Vieta's formulas are equations that connect some expressions of the roots of a polynomial equation to its coefficients. (See e.g. wikipedia)

I'll need to look that up.
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Thread 'Six Pencil Puzzle'

Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
View full post »

Similar threads

B Finding polynomials with given roots
Replies
14
Views
2K
I What type is a polynomial function?
Replies
7
Views
2K
A How Are Stieltjes Polynomials Related to Legendre Polynomials?
Replies
12
Views
2K
I Proof for interpolating polynomial and error approximation
Replies
6
Views
2K
B Why Is a Cubic Polynomial Called 'Third Degree'?
Replies
3
Views
2K
B About a definition: What is the number of terms of a polynomial P(x)?
Replies
48
Views
3K
MHB Find Cubic Function & Polynomial of Degree 3
Replies
5
Views
1K
I A doubt about the multiplicity of polynomials in two variables
Replies
8
Views
2K
MHB Area of the bounded regions between a straight line and a polynomial
Replies
1
Views
1K
MHB Roots of a Polynomial Function A²+B²+18C>0
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top