If cos^4 theta+alpha , sin^4 theta +alpha are the roots of the equation x^2+b(2x+1) =0 and cos^2 theta +beta ,sin^2 theta +beta are the roots of the equation x^2+4x+2=0 then b is equal to

Answers (1)

Solution:   We have ,

                     cos^4	heta+alpha , sin^4	heta+alpha   are the roots x^2+b(2x+1)=0

                     cos^2	heta+eta ,sin^2	heta+eta   are the roots    x^2+4x+2=0

              Rightarrow     cos^4	heta-sin^4	heta=cos^2	heta-sin^2	heta=cos 2	heta

            Rightarrow                       (-2b)^2-4b=(-4)^2-4	imes 2

           Rightarrow                       b^2-b-2=0Rightarrow b=-1,2

 

 

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