Question

alpha and beta are the zeroes of x2-(k+6)x+2(2k-1).Find the value of k if alpha +beta= 1/2 alpha.beta

Answer 1

$\\ {x}^{2} - (k + 6)x + 2(2k - 1) \\ \alpha + \beta = \frac{ - b}{a} \\ = k + 6 \\ \alpha \beta = 2(2k - 1) \\ from \: question \\ \alpha + \beta = \frac{1}{2} \alpha \beta \\ k + 6 = \frac{1}{2} (2(2k - 1)) \\ k + 6 = 2k - 1 \\ k - 2k = - 1 - 6 \\ - k = - 7 \\ k = 7 \: \: \: \: ans$