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 β γ + β γ α + γ α β is equal to

Step-by-step solution

Since α , β , γ are the roots of 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 β γ + β γ α + γ α β = α 2 β 2 + β 2 γ 2 + γ 2 α 2 α β γ = α β + β γ + γ α 2 - 2 α β γ α + β + γ α β γ = q 2 - 2 r p r