Solution:
Given equation, 4x²+3px+8=0
Here, a = 4, b = 3p, c = 8
Since roots are real,
So, b² - 4ac ≥ 0
(3p)² - 4 x 4 x 8 ≥ 0
9p² – 128 ≥ 0
9p² ≥ 128
p² ≥ 128/9
p ≥ ± 8√2/3
The value of p so that the equation 4x²-3px+9=0 has real roots is p ≥ 8√2/3 or p ≥ -8√2/3.