Question

a and ß are the roots of the quadratic polynomial p(x)=x^2-(k-6)x+2(2k-1).Find the value of k,if a+ß=1/2aß.

Answer 1

put these values in the eq.
$\alpha + \beta = \frac{k - 6}{1} \\ \alpha \beta = 2(2k - 1)$
$k - 6 = \frac{1}{2 \times 2(2k - 1) }$
$k - 6 = \frac{1}{4(2k - 1)}$
$4(2k - 1)(k - 6) = 1 \\ = ( 8k - 4)(k - 6) = 1 \\ 8 {k}^{2} - 48k - 4k + 24 - 1 = 0 \\ 8 {k}^{2} - 52k + 23 = 0$