Question

The values of k for which the quadratic equation 2x² – kx + k = 0 has equal roots are ______.

Answer 1

The values of k for which the quadratic equation 2x² – kx + k = 0 has equal roots are 0, 8.

Explanation:

For equal (repeated) roots the discriminant must be zero.

For 2x² – kx + k = 0,

 a = 2, b = –k, c = k,

So D = b² – 4ac

= (–k)² – 4 × 2 × k 

= k² – 8k

= k(k – 8)

= 0 

Hence k = 0 or k = 8.