Question

Let S be the set of all non-zero real numbers a such that the quadratic equation ax² − x + a = 0 has two distinct real roots x₁ and x₂ satisfying the inequality |x₁ − x₂| < 1. Which of the following intervals is (are) a subset(s) of S?

(a) (-1/2,-1/√5)

(b)  (-1/√5, 0)

(c) (0, 1/√5)

(d)  (1/√5, 1/2)

Answer 1

Correct option  (A) and (D).

αx² − x + α = 0 has two distinct real roots x₁ and x₂; |x₁ − x₂| < 1.

Therefore, intersection of Eqs. (1) and (2) gives