VITEEE 2012 Paper

Given equation x2 + px + q = 0 has roots a and α2
⇒ Sum = α + α2 = -p and Product = α3 = q
⇒ α (α + 1) = -p
⇒ α3 [α3 + 1 + 3α (α + 1)] = - p3
⇒ q(q + 1 - 3p) = - p3
⇒ p3 - (3p - 1) q + q2 = 0