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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^ (c) are in

Options

  1. AArithmetic-Geometric Progression
  2. BA.P.
  3. CG.P.
  4. DH.P.

Correct answer

B. A.P.

Step-by-step solution

f(x)=a x^2+b x+cf(1)=f(-1) a+b+c=a-b+c or b=0 f(x)=a x^2+c or f^ (x)=2 a x Now f^ (a) ; f^ (b) ; and f^ (c) are 2 a(a) ; 2 a(b) ; 2 a(c) . If a, b, c are in A.P. then f^ (a) ; f^ (b) and f^ (c) are also in A.P.

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