Let the roots of x3+ax2+bx+c=0 are α−1,α,α+1 as roots are in AP with common difference 1. Now, sum of roots =3α=−a....(i) Sum of product of roots taking two at a time
=(α−1)α+(α+1)α+(α−1)(α+1)=b
⇒3α2−1=b...(ii) and product of roots =α(α2−1)=−c ....(iii) From Eqs. (i), (ii) and (iii), we have