Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The value of ‘a’ for which the equation
x 3 – 3x + a = 0 has two different roots in [0, 1] is given by -
Text Solution
Verified by ExpertsThe correct answer is:
D
Let α , β be two different roots of ƒ(x) = 0 in [0, 1] where ƒ(x) = x 3 – 3x + a. Therefore, by Rolle’s theorem ƒ ′ (x) = 0 has a root between α and β , i.e. in (0, 1). But, ƒ ′ (x) = 0 ⇒ 3x 2 – 3 = 0 ⇒ x = ±1
∴ ƒ ′ (x) = 0 has no roots in (0, 1)
Hence the given equation has no root lying between 0 and 1 for any value of a.
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