Question

Let f(x) be a polynomial function of second degree. If f(1) = f (–1) and a₁, a₂, a₃ are in AP then f '(a₁), f '(a₂), f '(a₃) are in

• A. A.P.
• B. G.P.
• C. H.P.
• D. None of these

Answer 1

Answer: (A)

A.P.

Answer 2

Let f(x) = lx² + mx + n

f '(x) = 2lx + m

f(1) = f(–1)

l + m + n = l – m + n ; m = 0

f '(a₁) = 2la₁, f '(a_­2) = 2la₂ f '(a₃) = 2la₃

Now a₁, a₂, a₃ in AP

\ f '(a₁), f '(a₂), f '(a₃) are in A.P.