If polynomial p(x) = Ax^3 + Bx^2 + Cx + D vanishes at x = a - d, a, a + d, then prove that a^2 + D/aA 0. Here A, B, C, D are some constant. Please work the complete solution.

Question

If polynomial p(x) = Ax^3 + Bx^2 + Cx + D vanishes at x = a - d, a, a + d, then prove that a^2 + D/aA > 0. Here A, B, C, D are some constant. Please work the complete solution.