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CGP EDU Academic Team
Published on: August 13, 2026
The number of values of k for which the equation x 3 – 3x + k = 0 has two different roots lying in the interval (0, 1) are -
Text Solution
Verified by ExpertsThe correct answer is:
D
Let ƒ(x) = x 3 – 3x + k. Let, if possible, a, b ∈ (0, 1) be different roots of ƒ(x) = 0. ƒ(x) is continuous on [0, 1] and differentiable on (0, 1).
Also, ƒ = ƒ = 0
∴ By Rolle’s theorem there exists c ∈ (0, 1) such that
ƒ ′ = 0 ⇒ 3c 2 – 3 = 0 ⇒ c = ± 1
∴ no value of k satisfies the condition.
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