Question

Question 6
Value(s) of k for which the quadratic equation $2x^2$ - kx + k = 0 has equal roots is/are
(A) 0 only
(B) 4
(C) 8 only
(D) 0, 8​​​​​​

Answer 1

(D) is correct answer .

Given equation is $2x^2$ – kx + k = 0
On comparing with $a{x}^2$ + bx + c = 0, we get

A = 2, b = - k and c = k

For equal roots, the discriminant must be zero
i.e. D = $b^2$ – 4ac = 0
$\Rightarrow (-k{)}^2-4(2)k=0$
$\Rightarrow k^2-8k=0$
$\Rightarrow k(k-8)=0$
$\Rightarrow k=0,8$
Hence, the required values of k are 0 and 8 .