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

Step-by-step solution

The roots of the equation px 3 + qx 2 + r = 0 are α , β , γ i.e. α β + β γ + γ α = 0 ∴ α β β γ γ α β γ γ α α β γ α α β β γ Applying C 1 → C 1 + C 2 + C 3 α β + β γ + γ α β γ γ α α β + β γ + γ α γ α α β α β + β γ + γ α α β β &#94