Find the value of p for which the quadratic equation 4x2-3px+9=0 has real roots

Question

Find the value of p for which the quadratic equation 4x²-3px+9=0 has real roots

Answer 1

Given equation, 4x²-3px+9=0

Here, a = 4, b = -3p, c = 9

Since roots are real,

So, b² - 4ac ≥ 0

(-3p)² - 4 x 4 x 9 ≥ 0

9p² – 144 ≥ 0

9p² ≥ 144

p² ≥ 144/9

p² ≥ 16

p² ≥ 4²

p ≥ ±4

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