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Find the sum of the squares and the sum of the cubes of the roots of the equation x3 – px2 + qx – r = 0 in terms of p, q, r. |
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Answer» Let α, β, γ be the roots of the given equation then α + β + γ = p, αβ + βγ + γα = q, αβγ = r Sum of the squares of the roots is α2 + β2 + γ2 = (α + β + γ)2 – 2 (αβ + βγ + γα) = p2 – 2q Sum of the cubes of the roots is α3 + β3 + γ3 = (α + β + γ) (α2 + β2 + γ2 – αβ – βγ – γα) + 3αβγ = p(p2 – 2q – q) + 3r = p(p2 – 3q) + 3r |
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