Question

Let $f\left(x\right)=a{x}^2+bx+c$ such that $f\left(1\right)=f(-1)$ and a, b, c are in Arithmetic Progression.

What is the value of b?

• A. $-1$
• B. $0$
• C. $1$
• D. Cannot be determined due to insufficient data

Answer 1

The correct option is B $0$

$a,b,c$ are in A.P

$2b=a+c$ $\dots \left(i\right)$

$f\left(1\right)=f(-1)$

$a+b+c=a-b+c$

$b+b=b-b$ $\dots \left(i\right)$

$2b=0$

$\therefore b=0$