InterviewSolution
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InterviewSolution
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α, β ,γ are roots of x3 + ax2 + b = 0, then the value of||(α, β ,γ), (β, γ, α), (γ, α,β)| is(a) –a3 (b) a3– 3b(c) a3 (d) None of these |
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Answer» Correct option (c) a3 Explanation: α + β + γ = –a, α β + β γ + γ α = 0, α β γ = -b It can be shown that |(α, β ,γ), (β, γ, α), (γ, α,β)| = (α + β + γ)(α2 + β2 + γ2 - α β - β γ - γ α) = (α + β + γ)(α + β + γ)2 -3(α β + β γ + γ α)) = –(–a)((–a)2–3 x 0) = a3 |
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