Question

If alpha and beta are the zeroes of the polynomial fx=x square -x-k such that alpha-beta=9,find k

Answer 1

From the polynomial,
$\alpha + \beta = 1 \: \: and \: \: \alpha \beta = - k$
Given,
$\alpha - \beta = 9 \\ {( \alpha + \beta )}^{2} - {( \alpha - \beta )}^{2} = 4 \alpha \beta \\ {1}^{2} - {9}^{2} = 4 \times - k \\ k = 20$