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CGP EDU Academic Team
Published on: August 13, 2026
The equation x 3 – 3x + [a] = 0, where [.] denotes the greatest integer function, will have three real and distinct roots then find the set of all posible values of a.
Text Solution
Verified by ExpertsThe correct answer is:
A
(a ∈ [–1, 2)
f(x) = x 3 – 3x + k, k = [a]
f ′ (x) = 3(x – 1) (x + 1)
– 1 is maxima is 1 is minima
for three roots f(–1) f(1) < 0
⇒ (k + 2) (k – 2) < 0
k ∈ (–2, 2) ⇒ – 2 < [a] < 2
⇒ – 1 ≤ a < 2
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