Question

Let $f(x)$ be a second degree polynomial. If $f(1) = f(-1)$ and $p, q, r$ are in A.P., then $f'(p), f'(q), f'(r)$ are

• A. in A.P.
• B. in G.P.
• C. in H.P.
• D. neither in A.P. or G.P. or H.P.

Hint:

Whenever you are given conditions like $f(1) = f(-1)$ for a polynomial, check if it forces symmetry (like eliminating the $x$ term). For A.P. checks, remember the middle term must be the average of the two outer terms!