Find the non-zero value of k for which the roots of the quadratic equation
Question:

Find the non-zero value of $k$ for which the roots of the quadratic equation $9 x^{2}-3 k x+k=0$ are real and equal.

Solution:

The given equation is $9 x^{2}-3 k x+k=0$.

This is of the form $a x^{2}+b x+c=0$, where $a=9, b=-3 k$ and $c=k$.

$\therefore D=b^{2}-4 a c=(-3 k)^{2}-4 \times 9 \times k=9 k^{2}-36 k$

The given equation will have real and equal roots if D = 0.

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

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

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

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

But, k ≠ 0        (Given)

Hence, the required value of k is 4.