Question

Find the value of $m$ so that the quadratic equation $mx(5x-6)+9=0$ has two equal roots.

Answer 1

The given quadratic equation is $mx(5x-6)+9=0$
$\therefore 5m{x}^2-6mx+9=0\cdots \left(1\right)$
For equation (1) to have equal roots, the discriminant of the equation $\left(D\right)$ should be 0.
$\Rightarrow (-6m{)}^2-4\times 5m\times 9=0$
$\Rightarrow 36m^2-180m=0$
$\Rightarrow 36m(m-5)=0$
$\Rightarrow m=0orm-5=0$
$\Rightarrow$ $m=5$ (If $m=0$, then equation (1) will not be a quadratic equation)
Thus, the value of $m$ is $5$.