MHB What are Vieta's Formulas in Polynomial Functions?

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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
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I say the answer is A.

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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 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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