Question

If $-4$ is a common root for the quadratic equation $2x^2+px+8=0$ and $p(x^2+x)+k=0$ then find the value of $k$.

Answer 1

Given, $-4$ is a common root for the quadratic equation $2x^2+px+8=0$.....(1) and $p(x^2+x)+k=0$......(2).

Then $-4$ will satisfy equation (1), then we get,

$2.(-4{)}^2+p.(-4)+8=0$

or, $32-4p+8=0$

or, $p=10$.....(3).

Also $-4$ will satisfy equation (2) then we get,

$p.(16-4)+k=0$

or, $k=-12p$

or, $k=-120$. [ Using (3)]