AP EAPCET 19-Aug-2021 Shift 1 Paper

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