Question

if alpha and beta are the zeros of the polynomial kx2+4x+4,find the value of k such that (alpha +beta ) the whole square -2 alpha . beta=24

Answer 1

$\alpha + \beta = \frac{ - 4}{k} \: \: \: and \: \: \: \alpha \beta = \frac{4}{k} \\ {( \alpha + \beta )}^{2} - 2 \alpha \beta = 24 \\ \frac{16}{ {k}^{2} } - \frac{8}{k} = 24 \\ 3 {k}^{2} + k - 2 = 0 \\ (3k - 2)(k + 1) = 0 \\ k = \frac{3}{2} \: \: or \: \: - 1$