# Graph and Area

Calculus Level 4

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

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