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

Question

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

Answer 1

Given equation, 3x²-px+3=0 has real roots

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

So, b² - 4ac ≥ 0

(-p)² - 4 x 3 x 3 ≥ 0

p2 – 36 ≥ 0

p2 ≥ 36

p ≥ ± √36

p ≥ ± 2√15

The value of p so that the equation 3x²-px+3=0 has equal roots is 2√15