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Question

If α,β and γ are the real roots of the equation x3+5x2+9x6=0. Find the value of α2+β2+γ2.
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Solution

We know
(α+β+γ)2=α2+β2+γ2+2(αβ+βγ+γα) α2+β2+γ2=(α+β+γ)22(αβ+βγ+γα) = (5)22×9 = 25 - 18 = 7

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