Question

The values of a for which both the roots of the equation (1 − a²)x² + 2ax − 1 = 0 lie between 0 and 1 are given by

(A)  a > 2

(B)  1 < a < 2

(C)  − ∞ < a < ∞

(D)  None of these

Answer 1

Correct option (A)  a > 2

Given equation is (1 − a²)x² + 2ax − 1 = 0

Its discriminant is D = 4 and roots are 1/a - 1, 1/a + 1

Given,

⇒ a < −1 or a > 0

Hence, a > 0. From Eqs. (1) and (2), a > 2.  ...(2)