Find the value of k for which the quadratic equation 9x2 + 3kx + 4 = 0 has distinct roots.

Question

Find the value of k for which the quadratic equation 9x² + 3kx + 4 = 0 has distinct roots.

Answer 1

Given equation, 9x²+3kx+4=0

where, a = 9, b = 3k, c = 4

For distinct roots,

So, b² - 4ac > 0

(3k)² - 4 .9 .4 > 0

9k² - 144 > 0

9k² > 144

k² > 144/9

k² > 16

k² > 4²

k > 4

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