Question

Find the values of p for which the equation 3x² – px + 5 = 0 has real roots.

Answer 1

3x² – px + 5 = 0
Here, a = 3, b = -p, c = 5
∴ b² - 4ac
= (-p)² - 4 x 3 x 5
= p2 - 60
∴ Roots are real
∴ b² - 4ac ≥ 0
∴ p² - 60 ≥ 0
⇒ p² ≥ 60
⇒ ${\displaystyle p\ge \pm \sqrt{60}=\pm 2\sqrt{15}}$
∴ ${\displaystyle p\le -2\sqrt{15}\text{or}p\ge 2\sqrt{15}}$.