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Question

If α,β are the zeros of the polynomial f(x)=x23x+6, then find the value of 1α+1β+α2+β22αβ

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Solution

α+β=(3)=3
αβ=6
(α+β)24αβ=(αβ)2=924=15
1α+1β=α+βαβ=36=12
1α+1β+(αβ)2
1215
292

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