If the zeros of the polynomial f(x)=ax3+3bx2+3cx+d are in A.P.,prove that 2b3-3abc+a2d=0

Let A-D,A,A+D be the roots of the cubic polynomial.

Then,Sum of roots=(A-D)+A+(A+D)=3A=-3b/a

Thus,A=-b/a,Which is a root of the polynomial .

Hence,satisfies it,