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CGP EDU Academic Team
Published on: August 12, 2026
The equation x 3 − − 3x + [a] = 0, where [.] denotes the greatest integer function, will have real and distinct roots if
Text Solution
Verified by ExpertsThe correct answer is:
D
Let f(x) = x 3 − − 3x + 1 ⇒ ⇒ f(x) = 3(x – 1)(x + 1).
Clearly x = − − 1 and x = 1 are the points of local maxima and local minima respectively for y = f(x). Now f(x) = 0 will have real and distinct roots if f(1).f(-1) < 0 ⇒ ⇒ ([a] + 2) ([a] - 2) < 0
⇒ ⇒ − − 2 < [a] < 2
⇒ ⇒ a ∈ ∈ [-1,2)
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