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 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
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
988
MHB Roots of a Polynomial Function A²+B²+18C>0
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top