Question

What is the set of values of p for which the roots of the equation 3x^2 + 2x + p(p – 1) = 0 are of opposite sign?

(a) (-∞, 0)

(b) (0, 1)

(c) (1, ∞)

(d) (0, ∞)

This question was posed to me in semester exam.

The doubt is from Applications of Quadratic Equations in portion Complex Numbers and Quadratic Equations of Mathematics – Class 11

Answer 1

Correct choice is (b) (0, 1)

The best I can explain: Since the roots of the given equation are of opposite sing,

So, products f the roots < 0

 p(p – 1) / 3 < 0

 p(p – 1) < 0

 0 < p < 1

For real and distinct roots ½ – √21/ 6 < p < ½ + √21/6