Q146 / 225 · JEE Main 2003 · Mathematics

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

  • A
    Arithmetic-Geometric Progression
  • Correct answer
    B
    A.P.
  • C
    G.P.
  • D
    H.P.

Solution

$f(x)=a x^2+b x+c$ $f(1)=f(-1) \Rightarrow a+b+c=a-b+c$ or $b=0$ $\therefore f(x)=a x^2+c$ or $f^{\prime}(x)=2 a x$ Now $f^{\prime}(a) ; f^{\prime}(b) ;$ and $f^{\prime}(c)$ are $2 a(a) ; 2 a(b) ; 2 a(c)$. If $a, b, c$ are in A.P. then $f^{\prime}(a) ; f^{\prime}(b)$ and $f^{\prime}(c)$ are also in A.P.

Hence, the correct answer is option: 'B'.

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