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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.
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