Let f(x) be a polynomial function of second degree. If f(1) = f(-1) and a, b, c are in A.P., then f'(a) , f'(b) and f'(c) are in: - Mathematics MCQ AIEEE-CBSE-ENG-03 2026 | ExamTest.live

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Let f (x) be a polynomial function of second degree. If f (1) = f (- 1) and a, b, c are in A.P., then f^{'} (a), f^{'} (b) and f^{'} (c) are in:

Solution & Step-by-step Explanation

Let f (x) = A x^{2} + B x + C . f (1) = A + B + C and f (- 1) = A - B + C .Given f (1) = f (- 1) ⟹ B = 0 .So, f (x) = A x^{2} + C .The derivative is f^{'} (x) = 2 A x .Given a, b, c are in A.P., let b - a = c - b = d .Then: f^{'} (a) = 2 A a f^{'} (b) = 2 A b f^{'} (c) = 2 A c Check differences: f^{'} (b) - f^{'} (a) = 2 A b - 2 A a = 2 A (b - a) = 2 A d f^{'} (c) - f^{'} (b) = 2 A c - 2 A b = 2 A (c - b) = 2 A d Since the differences are equal, f^{'} (a), f^{'} (b), f^{'} (c) are in A.P.

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Let f (x) be a polynomial function of second degree. If f (1) = f (- 1) and a, b, c are in A.P., then f^{'} (a), f^{'} (b) and f^{'} (c) are in:

A.P.

G.P.

H.P.

arithmetic-geometric progression

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