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Relationship Between Zeroes and Coefficients of a Quadratic Polynomial

If α and ...

Question

If $α$ and $β$ are zeroes of the polynomial $(x) = x^{2} - x - k$ , such that $α - β = 9$ , find $k$ .

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Solution

$f (x) = x^{2} - x - k = 0$
$α + β = 1 α β = - k$
$α - β = 9 α β = - k$
$α = 55 (- 4) = - k$
$β = - 4 k = 20$
$∴ k = 20$

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