Question:

Find the values of $k$ for which the quadratic equation $9 x^{2}-3 k x+k=0$ has equal roots.

Solution:

It is given that the quadratic equation $9 x^{2}-3 k x+k=0$ has equal roots.

$\therefore D=0$

$\Rightarrow(-3 k)^{2}-4 \times 9 \times k=0$

$\Rightarrow 9 k^{2}-36 k=0$

$\Rightarrow 9 k(k-4)=0$

$\Rightarrow k=0$ or $k-4=0$

$\Rightarrow k=0$ or $k=4$

Hence, 0 and 4 are the required values of k.