Question

If $2$ is a root of the equation $x^2+kx+12=0$ and the equation $x^2+kx+q=0$ has equal roots, find the value of $q$.

Answer 1

$x^2+kx+12=0$

root of the above equation is 2

$2^2+k\left(2\right)+12=0$

$4+2k+12=0$

$2k=-16$

$k=-8$

$x^2+kx+q=0$

$x^2-8x+q=0$

condition for equal roots is $b^2=4ac$

$\therefore (-8{)}^2=4(1\left)\right(q)$

$64=4q$

$\therefore q=16$