Let f(x) be a polynomial of second degree. If f(1) = f(-1) and a, b, care in A.P., then f'(a), f'(b), f'(c) are in
Answer & explanation
Correct answer: option 2
Let $f(x)=p x^2+q x+r$. Then,
$f(1)=f(-1) \Rightarrow p+q+r=p-q+r \Rightarrow q=0$
∴ $f(x)=p x^2+r$
$\Rightarrow f'(x)=2 p x \Rightarrow f'(a)=2 a p, f'(b)=2 b p$ and $f'(c)=2 c p$
Now,
a, b, c are in A.P.
⇒ 2ap, 2bp, 2cp are in AP.
⇒ f'(a), f'(b), f'(c) are in AP.