Question

if alpha and beta are zeros of quadratic polynomial 2 X square + 5 x + K find K such that alpha + beta the whole square minus alpha beta is equal to 24

Answer 1

From the polynomial,
$\alpha + \beta = \frac{ - 5}{2} \\ \alpha \beta = \frac{k}{2}$
Given
${( \alpha + \beta )}^{2} - \alpha \beta = 24 \\ {( \frac{ - 5}{2} )}^{2} - \frac{k}{2} = 24 \\ 25 - 2k = 96 \\ k = \frac{ - 71}{2}$