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The quadratic x^2 +ax+b+1=0 has roots which are positive integers then (a^2 +b^2) can be equal

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Solution: x^2+ax+b+1=0 has possible roots alpha  and eta

      \ \ Rightarrow hspace1cm alpha +eta=-a hspace0.2cmand hspace0.2cmalpha eta=b+1\ \ Rightarrow hspace1cm(alpha+eta)^2+(alphaeta-1)^2=a^2+b^2

      (alpha+eta)^2+(alphaeta-1)^2=a^2+b^2=(alpha^2+1)(eta^2+1)          

         

Posted by

Deependra Verma

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