Question 1

What does Vieta's theorem state?

Accepted Answer

For ax²+bx+c=0 with roots x₁ and x₂: x₁+x₂ = −b/a and x₁·x₂ = c/a.

Question 2

How to apply Vieta's theorem to x²+px+q=0?

Accepted Answer

When a=1: x₁+x₂ = −p and x₁·x₂ = q. For example x²−5x+6=0: sum = 5, product = 6, roots are 2 and 3.

Question 3

What is Vieta's theorem used for?

Accepted Answer

It lets you find or verify the roots of a quadratic equation without solving it directly, and to write an equation whose roots you already know.

Vieta's Theorem

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