Domain of f(x) = l n (ax 3 + (a + b)x 2 + (b + c)x + c), wh…

Maths Functions, Limits, Continuity and Differentiability General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Domain of f(x) = l n (ax 3 + (a + b)x 2 + (b + c)x + c), where a > 0, b 2 - 4ac = 0, is

(-1, ∞ ∞ ) ~

(1, ∞ ∞ ) ~

( − − 1, 1) ~

None of these

Text Solution

Verified by Experts

The correct answer is:

We must have

ax 3 + (a + b)x 2 + (b + c)x + c > 0

⇒ ⇒ ax 2 (x + 1) + bx(x + 1) + c(x + 1) > 0

⇒ ⇒ (x + 1) (ax 2 + bx + c) > 0

⇒ ⇒ a(x + 1) (ax 2 + bx + c) > 0

⇒ ⇒ a(x+ 1) > 0 as b 2 = 4ac

⇒ ⇒ x > − − 1 and ≠ ≠

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