Question

The set of values of p for which the roots of the equation

3x² + 2x + p(p – 1) = 0 are of opposite sign is

• A. (–∞, 0)
• B. (0, 1)
• C. (1, ∞)
• D. (0, ∞)

Answer 1

Answer: (B)

(0, 1)

Answer 2

Since the roots of the given equation are of opposite sign, product of the roots < 0

⇒ $\frac{p(p - 1)}{3} < 0$ ⇒ p(p – 1) < 0 ⇒ 0 < p < 1.

For real roots

$1 - \frac{2}{\sqrt{3}} \leq p \leq 1 + \frac{2}{\sqrt{3}}$ ⇒ 0 < p < 1