Choose the correct answer from the given four options in the following questions:
Values of $ k $ for which the quadratic equation $ 2 x^{2}-k x+k=0 $ has equal roots is
(A) 0 only
(B) 4
(C) 8 only
(D) 0,8

To do:

We have to find the correct answer.

Solution:

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

Comparing with $a x^{2}+b x+c=0$, we get,

$a=2, b=-k$ and $c=k$

We know that,

For equal roots, the discriminant must be zero.

Therefore,

$D=b^{2}-4 a c=0$

$(-k)^{2}-4(2) k=0$

$k^{2}-8 k=0$

$k(k-8)=0$

$k=0$ or $k=8$

Hence, the required values of $k$ are 0 and 8.