f(x)=x3+ax2+bx+c Let roots of f(x) are α,β,γ and since roots are in AP. ∴‌‌2β=α+γ Now, Sum of roots α+β+γ=−a or 2β+β=−a or β=−‌
a
3
It is given that, roots are integers. ∴β is an integer when a is multiple of 3 . Option (a), (c) and (d) are multiple of 3 . ⇒‌‌a≠1214