If α and β are roots of the equation x2−3x+a=0 and γ and δ are roots of the  equation x2−12x+b=0 and α,β,γ,δ form an increasing  GP, then the values  of a and b are respectively

 If α and β are roots of the equation x23x+a=0 and γ and δ are roots of the  equation x212x+b=0 and α,β,γ,δ form an increasing  GP, then the values  of a and b are respectively

  1. A

    2,16

  2. B

    4,8

  3. C

    2,32

  4. D

    None of these

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    Solution:

    α,β,γ,δ are in GP.

    Let α=A,β=Ar,γ=Ar2,δ=Ar3

    α and β are the roots of the equation x23x+a=0,
    then  

    γ+δ=12Ar2(1+r)=12 ....(ii)

    On solving Eqs. (i) and (ii), we get

        A=1,r=2

        α=1,β=2,γ=4,δ=8    a=αβ=1×2=2 and     b=γδ=4×8=32

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