Question

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, find the value of p and k.

Answer 1

It is given that -4 is a root of the equation $x^2+px-4=0$.

Then, -4 must satisfy the equation,

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

$16-4p-4=0$

$4p=12$

$p=3$

Now, the equation $x^2+px+k=0$ has equal roots

Therefore,

Discriminant, $D=0⟹b^2-4ac=0$

$p^2-4k=0$

$9-4k=0$

$k=\frac{9}{4}$

Therefore, $p=3$ and $k=\frac{9}{4}$.