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Relationship between Zeroes and Coefficients of a Polynomial

If alpha and ...

Question

If alpha and beta are the zeroes of the polynomial $x^{2} - 6 x + a$ . Find alpha if beta = -2.

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Solution

$α$ and $β$ are roots of $x^{2} - 6 x + a$
$β = - 2$
$α + β = 6$ $α β = a$
$α - 2 = 6$ $β (- 2) = a$
$\Rightarrow α = 8$ $\Rightarrow a = - 16$

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