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  • Let alpha and beta be the roots of x^2 -3 x + p =0 and gamma and delta be the roots of x^2 -6x +q=0 . if alpha , beta , gamma and delta forms geometric progression then the ratio (2q+p): (2q-p) is

Let alpha and beta be the roots of x^2 -3 x + p =0 and gamma and delta be the roots of x^2 -6x +q=0 . if alpha , beta , gamma and delta forms geometric progression then the ratio (2q+p): (2q-p) is

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Solution:    

              x^2-3x +p=0   Rightarrow    alpha ,eta    be the roots 

       Rightarrow        (alpha +eta )=(alpha+alpha r)=3      ...........(1)

               x^2-6x+q=0   Rightarrow     gamma , delta   be the roots

       Rightarrow      (gamma+delta)=(alpha r^2+alpha r^3)=6     ..........(2)

      ecause         alpha, eta , gamma, delta   are in G.P

     From   Equation    frac(2)(1)    We get

              r^2=2.

  Therefore          frac(2q+p)2q-p=frac2r^5+r2r^5-r=frac2r^4+12r^4-1=frac97.       

Posted by

Deependra Verma

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