If α,β are the roots of the equation x2−3x+5=0 and γ,δ are the roots of the equation x2+5x−3=0, then the equation whose roots are αγ+βδ and αδ+βγ is

If α,β are the roots of the equation x23x+5=0 and γ,δ are the roots of the equation x2+5x3=0, then the equation whose roots are αγ+βδ and αδ+βγ is

  1. A

    x215x158=0

  2. B

    x2+15x158=0

  3. C

    x215x+158=0

  4. D

    x2+15x+158=0

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    Solution:

    α+β=3,αβ=5,γ+δ=(5),γδ=(3)

    Sum of roots

     =(αγ+βδ)+(αδ+βγ) =(α+β)(γ+δ)=3×(5)=(15)

    Product of roots

     =(αγ+βδ)(αδ+βγ) =α2γδ+αβγ2+βαδ2+β2γδ =γδ(α2+β2)+αβ(γ2+δ2)

     =3(α2+β2)+5(γ2+δ2) =3[(α+β)22αβ]+5[(γ+δ)22γδ] =3[910]+5[25+6]=158

    Required equation is x2+15x+158=0

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