Question

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

• A. $A.P$
• B. $G.P$
• C. $H.P$
• D. arithmetic-geometric progression

Answer 1

Answer: (A)

$A.P$

Answer 2

$f (x) = ax^2 + bx + c$ $f (1) = a + b + c$ $f (- 1) = a - b + c$ $? a + b + c = a - b + c$ also $2b = a + c$ $f' (x) = 2ax + b = 2ax$ $f' (a) = 2a^2$ $f' (b) = 2ab$ $f' (c) = 2ac$ $? AP.$