Question

if the roots of the quadratic equation 2kx² + (2a+b)x - ab = 0 are (-2,a) the value of k is?

Answer 1

Answer:

$k = \frac{b}{4}$

Step-by-step explanation:

$2k {x}^{2} + (2a + b)x - ab = 0 \\ \\ sum \: of \: the \: roots = - 2 - a = \frac{ - (2a + b)}{2k} \\ \\ - 4k - 2ka = - 2a - b \: \: \: \: \: \: ...(i) \\ \\ \\ \\ product \: of \: the \: roots = - 2a = \frac{ - ab}{2k} \\ \\ 4ak = ab \\ \\ then \: \: \: k = \frac{b}{4} \\ \\ \: \: and \: \: a = 0 \\ \\ from \: \: (i )... \\ \\ - 4k = - b \\ \\ k = \frac{b}{4} .$