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Question

Find a cubic polynomial with sum, sum of product of zeros taken 2 at the timeand product of zeros 5, -2 and -24 respectively.

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Solution

Let α,β and γ be the roots od the cubic polynomial
Given (α+β+γ)=2
(αβ+βγ+γα)=7 and (αβγ)=14
The cubic polynomial with roots α,β and γ is x3(α+β+γ)x2+(αβ+βγ+γα)x(αβγ)=0
x3(5)x2+(2)x(24)=0x35x22x+24=0

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