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Question
A cubic polynomial with sum of its zeroes, sum of the product of its zeroes taken two at a time and the product of its zeroes as 2, -7, -14 respectively, is __________.
A cubic polynomial with sum of its zeroes, sum of the product of its zeroes taken two at a time and the product of its zeroes as 2, -7, -14 respectively, is __________.
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Solution
The correct option is B x3−2x2−7x+14
For a given cubic polynomial if α,β and γ are the zeroes, then the polynomial can be expressed asx3−(α+β+γ)x2+(αβ+αγ+βγ)x−αβγHere, α+β+γ=2αβ+βγ+αγ=−7 andαβγ=−14Therefore the cubic polynomial is x3−2x2−7x+14Therefore,Option D is correct.
For a given cubic polynomial if α,β and γ are the zeroes, then the polynomial can be expressed as
x3−(α+β+γ)x2+(αβ+αγ+βγ)x−αβγ
Here, α+β+γ=2
αβ+βγ+αγ=−7 and
αβγ=−14
Therefore the cubic polynomial is x3−2x2−7x+14
Therefore,Option D is correct.
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