Let α , β , γ be the roots of the equation x 3 + p x + q = 0 and f x = 3 p 2 x 2 + p 2 x + 3 q . Then ∑ α 2 β + ∑ α 4 =

Question

Let α , β , γ be the roots of the equation x 3 + p x + q = 0 and f x = 3 p 2 x 2 + p 2 x + 3 q . Then ∑ α 2 β + ∑ α 4 =, f 1, f - 1, f 0, f 2

MARKS App · Accepted Answer

Given that α , β , γ are roots of x 3 + p x + q = 0 α + β + γ = 0 , α β + β γ + γ α = p & α β γ = - q α 2 β + β 2 γ + γ 2 α + α 4 + β 4 + γ 4 = - q α γ + - q β α + - q γ β + α 4 + β 4 + γ 4 = f - 1 .

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