Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let f(x) be a polynomial function of second degree. If f(1)
= f (–1) and a 1 , a 2 , a 3 are in AP then f '(a 1 ), f '(a 2 ), f '(a 3 ) are in
Text Solution
Verified by ExpertsThe correct answer is:
A
Let f(x) = λ x 2 + mx + n
f '(x) = 2 λ x + m
f(1) = f(–1)
λ + m + n = λ – m + n ; m = 0
f '(a 1 ) = 2 λ a 1 , f '(a 2 ) = 2 λ a 2 f '(a 3 ) = 2 λ a 3
Now a 1 , a 2 , a 3 in AP
∴ f '(a 1 ), f '(a 2 ), f '(a 3 ) are in A.P.
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