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  • If a+b+c=0 and a,b ,c are rational . Prove that the roots of equation ( b+c-a)x^2 +(c+a-b)x+(a+b-c)=0 are rational .

If a+b+c=0 and a,b ,c are rational . Prove that the roots of equation ( b+c-a)x^2 +(c+a-b)x+(a+b-c)=0 are rational .

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Solution:  Given equation is 

                              (b+c-a)x^2+(c+a-b)x+(a+b-c)=0

                ecause               (b+c-a)+(c+a-b)+(a+b-c)=a+b+c=0

                  herefore      x=1  is a root of equation  , let other root of equation is alpha

                  Rightarrow            1 imes alpha =fraca+b-cb+c-a=frac-c-c-a-a=fracca

                  Hence , both roots of equation  are rational.     

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Deependra Verma

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