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

★ QUADRATIC RESOLUTION ★

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