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# Vieta's Formula

Vieta's formula relates the coefficients of polynomials to the sum and products of their roots. This can provide a shortcut to finding solutions in more complicated algebraic polynomials.

# Vieta's Formula - Quadratics

What is the product of roots of the quadratic equation

$2 x^2 - 6 x + 36 = 0,$

If the two roots of the quadratic equation $$x^2-12x-2=0$$ are $$\alpha$$ and $$\beta$$, what is $$\alpha^2+\beta^2$$?

The difference between the two roots of the quadratic equation $x^2+Ax+B=0$ is $$12$$ and the larger root is $$3$$ times the smaller root. What is the value of $$A+B$$?

What are the sum of roots of the quadratic equation

$x^2 - 9 x + 15 = 0?$

Let $$\alpha$$ and $$\beta$$ be the two roots of the quadratic equation $x^2-16x+63=0.$ What is the value of $$\alpha+\beta+\alpha\beta$$?

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