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  • If alpha ,beta and gamma are roots of x^3-2x+1=0, then the value of sigma (1 / alpha +beta -gamma) is

If alpha ,beta and gamma are roots of x^3-2x+1=0, then the value of sigma (1 / alpha +beta -gamma) is

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Solution:  We have ,  x^3-2x+1=0

         Rightarrow        sum frac1alpha+eta -gamma =frac1alpha+eta -gamma+frac1alpha-eta+gamma +frac1-alpha+eta+gamma

        Rightarrow        alpha+eta+gamma =0,alpha eta+eta gamma+alpha gamma=-2,alpha eta gamma=1

     Hence , sum frac1alpha+eta-gamma=frac(-2eta)(-2alpha)+(-2gamma)(-2alpha)+(-2gamma)(-2eta)(-2gamma)(-2eta)(-2alpha)=frac4(-2)8(1)=-1.      

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Deependra Verma

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