Find the nonzero value of k for which the roots of the quadratic equation 9x2 – 3kx + k = 0 are real and equal.
Given equation is 9x2 – 3kx + k = 0
Comparing with standard quadratic equation ax2 + bx + c = 0
a = 9 b = – 3k c = k
Given that the roots of equation are real and equal
Thus D = 0
Discriminant D = b2 – 4ac = 0
(– 3k)2 – 4.9.k = 0
9 k2 – 36k = 0
9k(k – 4) = 0
9k = 0 or(k – 4) = 0
k = 0 or k = 4
But given k is non zero hence k = 4 for which roots of the quadratic equation are real and equal.