Question

Find the nonzero value of k for which the roots of the quadratic equation 9x² – 3kx + k – 0 are real and equal.

Answer 1

9x² – 3kx + k = 0

Compare given equation with the general form of quadratic equation, which is ax² + bx + c = 0

Here a = 9, b = -3k, c = k

Find discriminant:

D = b² – 4ac

= (-3k)² – 4 x 9 x k

= 9k² – 36k

Since roots are real and equal (given)

Put D = 0

9k² – 36k = 0

9k (k – 4) = 0

Either, k = 0 or k – 4 = 0

As, value of k is non-zero:

So, k = 4