Graph and Area

$f(x)=ax^3+bx^2+cx+d$ , $f' (1)=f' (-1)=0$ and $a>0$

The region bounded by $x$ -axis and $f(x)$ are $''A_1,A_2,A_3''$ such that $A1$ and $A3$ are in $IV$ and $II$ quadrant respectively.

If $f(x)$ has roots $a_1,a_2,a_3$ , such that $a_1>a_2$ and $a1>0$ Also $(a_1,a_2,a_3)$ , $(a_1^2,a_2^2,a_3^2)$ , $(a_1^4,a_2^4,a_3^4)$ , each triplets are in an arithmetic progression .

Then which of the following must be true?