Find the value of p for which the equation 3x2-px+5=0 has real roots

Question

Find the value of p for which the equation 3x²-px+5=0 has real roots

Answer 1

Given equation, 3x²-px+5=0

Here, a = 3, b = -p, c = 5

Now, b² - 4ac ≥ 0

(-p)² - 4 x 3 x 5 ≥ 0

p² - 60 ≥ 0

p² ≥ 60

p ≥ √60

p ≥ ±2√15

The value of p so that the equation 3x²-px+5=0 has equal roots are ±2√15.