Question

The value of ‘a’ for which x³ – 3x + a = 0 would have two distinct roots in (0, 1) is –

• A. 2
• B. –2
• C. 4
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Let ƒ(x) = x³ – 3x + a

ƒ¢(x) = 3x² – 3 = 0 ̃ x = ± 1

ƒ¢¢(x) = 6x

ƒ¢¢ (x) > 0 at x = 1 and ƒ¢¢(x) < 0 at x = –1

Thus, x = 1 is point of minima and x = –1 is point of maxima.

Hence either one root lies in [–1, 1] or no root lies in [–1, 1]. So no such value exist for which the given condition is possible.