Question

If the equation $9x^2+6kx+4=0$ has equal roots, then find the value of $k$.

Answer 1

Given, the roots of quadratic equation $9x^2+6kx+4=0$ are real and equal.
Discriminant, $\Delta =b^2-4ac$
$\Delta =36k^2-4\left(4\right)\left(9\right)=36k^2-4\left(36\right)$
The roots of quadratic equation are real
$\Delta =0$
$36k^2-4\left(36\right)=0$
$k^2-4=0$
$k^2=4$
$k=\sqrt{4}$
and equal then $\therefore k=\pm 2$