Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If f(x) = 
x 3 + (a – 3) x 2 + x + 5 is a one-one function, then number of possible integral values of a is
Text Solution
Verified by ExpertsThe correct answer is:
7
(7)
Sol. f(x) = 
x 3 + (a – 3) x 2 + x + 5 ⇒ f ′ (x) = (4a – 7) x 2 + 2(a – 3) x + 1
D ≤ 0 for all x ∈ R ⇒ x ∈ R D ≤ 0
4(a – 3) 2 – 4 (4a – 7) ≤ 0 ⇒ a 2 + 9 – 6a – 4a + 7 ≤ 0
a 2 – 10a + 16 ≤ 0 ⇒ (a – 8) (a – 2) ≤ 0
or a ∈ [2, 8] ⇒ f ′ (x) is always +ve for a ∈ [2, 8]
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