Let Alpha and Beta be the zeros of the cubic polynomial x^3 + ax^2 + bx + c satisfying the relation Alpha * Beta = 0. Prove that : c^2 + ac + b + 1 = 0.

Question

Let Alpha and Beta be the zeros of the cubic polynomial x^3 + ax^2 + bx + c satisfying the relation Alpha * Beta = 0. Prove that : c^2 + ac + b + 1 = 0.
Please work the complete solution.