Value(s) of k for which the quadratic

Question:

Value(s) of k for which the quadratic equation 2x2 -kx + k = 0 has equal roots is/are

(a) 0                          

(b) 4                           

(c) 8                         

(d) 0, 8

Solution:

(d)

Given equation is 2x2 – kx + k- 0

On comparing with ax2 + bx + c = 0, we get

a = 2, b= – k and c = k

For equal roots, the discriminant must be zero.

i.e., $D=b^{2}-4 a c=0$

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

$\Rightarrow \quad k^{2}-8 k=0$

$\Rightarrow \quad k(k-8)=0$

$\therefore \quad k=0,8$

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

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