# 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

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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.

Updated on 10-Oct-2022 13:27:26