Question

Determine the value of k, if -4 is a root of the quadratic equation $x^2+px-4=0$ and the quadratic equation $x^2+px+k=0$ has equal roots?

Answer 1

Consider the given equation (1),

$x^2+px-4$$=0$

Put $x=-4$ and we get, ${(-4)}^2+px-4$$=0$

$\Rightarrow 16-$$p-4$$=0$

$\Rightarrow -$$p=-12$

$\Rightarrow p=3$

Put the value of $p$ in given equation (2),

$x^2+px+k=0$

${(-4)}^2+3\times (-4)+k=0$

$\Rightarrow 16-12+k=0$

$\Rightarrow k=-4$

Hence, this is the answer.