If α , β and γ are the roots of the equation x 3 - p x 2 + q x - r = 0 , then the value of α 2 β + α 2 γ + β 2 α + β 2 γ + γ 2 α + γ 2 β is equal to

Step-by-step solution

x 3 - p x 2 + q x - r = 0 α + β + γ = p α β + β γ + γ α = q α β γ = r ⇒ α 2 β + α 2 γ + β 2 α + β 2 γ + γ 2 α + γ 2 β = α + β + γ α β + β γ + γ α - 3 α β γ = p q - 3 r