Let α , β , γ be the three roots of the equation x 3 + b x + c = 0 if β γ = 1 = - α then b 3 + 2 c 3 - 3 α 3 - 6 β 3 - 8 γ 3 is equal to

Step-by-step solution

Given that roots of x 3 + b x + c = 0 are α ,   β ,   γ Also given that β γ = 1 = - α ⇒ α = - 1 . . . ( i ) Now let us apply the relation between the roots of the cubic equation with the coefficients. ⇒ α + β + γ = 0 . . . ( ii ) ⇒ α β γ = - c . . . ( iii ) ⇒ - 1 1 = - c ∴ c = 1 . . . ( iv ) On substituting the value of α = - 1 in eq i i we get, β + γ = 1 . . . ( v ) ∵ α β + β