Choose the correct answer from the given four options in the foll… - Vidyadip

MCQ

Choose the correct answer from the given four options in the following questions: Values of $k$ for which the quadratic equation $2x^2- kx + k = 0$ has equal roots is :

A
$0$ only.
B
$4.$
C
$8$ only.
✓
$0, 8.$

✓

Answer

Correct option: D.

$0, 8.$

Given equation is $2 x^2-k x+k=0$
On comparing with $a x^2+b x+c=0$, we get
$a = 2, b = -k$ and $c = k$
For equal roots, the discriminant must be zero.
i.e., $D=b^2-4 a c=0$
$\Rightarrow(-k)^2-4(2) k=0$
$\Rightarrow k^2-8 k=0$
$\Rightarrow k(k - 8) = 0$
$\therefore k = 0, 8$
Hence, the required values of $k$ are $0$ and $8$.

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