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

Question

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

Answer 1

Given equation, 9x² + 3kx + 4=0

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

Since roots are real,

So, b² - 4ac ≥ 0

(3k)² - 4 x 9 x 4 ≥ 0

9k² – 144 ≥ 0

9k² ≥ 144

k² ≥ 144/9

k² ≥ 16

k² ≥ 4²

k ≥ ±4

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