Question

If the following quadratic equation has two equal and real roots then find the value of $k$:
$k{x}^2-24x+16=0$

Answer 1

$k{x}^2-24x+16=0$

If the roots of a quadratic equation are equal then $D=0$.

Now,

$D=\sqrt{b^2-4ac}$

$\Rightarrow 0=(24{)}^2-4(16\left)\right(k)$

$\Rightarrow 0=(24{)}^2-4(16)k$

$\Rightarrow k=\frac{(24{)}^2}{4\left(16\right)}$

$\Rightarrow k=9$

Hence, the value of $k$ is equal to $9$.