What are Vieta's Formulas in Polynomial Functions?

mathland · Jan 28, 2021

I say the answer is A.

Multiple-choice question titled Polynomial Function: write the quadratic equation whose roots are 1 and 1/alpha. Options A to D: x^2 - (x - 1)x + 1/alpha = 0; alpha x^2 - (x + 1)x - 1 = 0; alpha x^2 - (alpha + 1)x + 1 = 0; x^2 - (alpha + 1)x + 1 = 0.

topsquark · Jan 28, 2021

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

mathland · Jan 29, 2021

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?

jonah1 · Jan 29, 2021

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!

Theia · Jan 30, 2021

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)

mathland · Jan 31, 2021

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.

What are Vieta's Formulas in Polynomial Functions?

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