Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Let f(x) be a quadratic expression which is positive for all real x. If g(x) = f(x) + f ′ (x) + f ′′ (x), then for any real x -
Text Solution
Verified by ExpertsThe correct answer is:
A
Let f(x) = ax 2 + bx + c > 0
⇒ a > 0, b 2 – 4ac < 0
g(x) = (ax 2 + bx + c) + (2ax + b) + 2a
= ax 2 + (2a + b) x + 2a + b + c
Now a > 0
D = (2a + b) 2 – 4a (2a + b + c)
= b 2 – 4ac ; D < 0 ⇒ g(x) > 0
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