Find the value of k for which the quadratic equation 9x2 - 3kx +k = 0 has equal roots.

Question

Find the value of k for which the quadratic equation 9x² - 3kx +k = 0 has equal roots.

Answer 1

Given equation, 9x² - 3kx + k=0

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

Now, b² - 4ac = 0

(-3k)² - 4 .9.k=0

9k² - 36k=0

9k(k-4)=0

9k=0, k-4=0

k=0,   k=4

The value of k so that the equation 9x² - 3kx + k=0 has equal roots is 0 or 4