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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)=0⇒x3−5x2−2x+24=0
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)=0⇒x3−5x2−2x+24=0
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