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Question
If α.β are the roots of x2+ax−b=0 and γ,δ are the roots of x2+ax+b=0 then
(α−γ)(α−δ)(β−δ)(β−γ)
If α.β are the roots of x2+ax−b=0 and γ,δ are the roots of x2+ax+b=0 then
(α−γ)(α−δ)(β−δ)(β−γ)
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Solution
The correct option is A 4b2
α+β=−aαβ=−b,→(1)γ+δ=−aγδ=b→(2)now(α−γ)(γ−δ)(β−δ)(β−γ)=[α2−αγ+αδ+γδ][β2−βδ−βγ+δγ]=[α2−α(γ+δ)+δγ][β2−β(δ+γ)+δγ]=[α2+aα+b][β2+βα+b]from(1)asαandβarerootsofx2+ax−b=0α2+aα−b=0α2+aα=balsoβ2+aβ=b=(b+b)(b+b)=4b2
α+β=−aαβ=−b,→(1)γ+δ=−aγδ=b→(2)now(α−γ)(γ−δ)(β−δ)(β−γ)=[α2−αγ+αδ+γδ][β2−βδ−βγ+δγ]=[α2−α(γ+δ)+δγ][β2−β(δ+γ)+δγ]=[α2+aα+b][β2+βα+b]from(1)asαandβarerootsofx2+ax−b=0α2+aα−b=0α2+aα=balsoβ2+aβ=b=(b+b)(b+b)=4b2
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