Question

Find the value of $k$ for which the given equation has equal roots. Also, find the roots.
$9x^2-24x+k=0$

Answer 1

The given equation is $9x^2-24x+k=0$

Here, $a=9,b=-24,c=k$

$\therefore D=b^2-4ac={(-24)}^2-4\times 9\times k=576-36k$

The given equation will have real and equal roots, if
$D=0\Rightarrow 576-36k=0\Rightarrow k=16$

Putting $k=16$ in the given equation, we get
$9x^2-24x+k=0\Rightarrow {(3x-4)}^2=0\Rightarrow x=\frac{4}{3}$

Hence, both the roots of the given equation are equal to $\frac{4}{3}$