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  • If a is not equal to b and difference between the roots of the equation x^2+ax+b=0 and x^2+bx+a=0 is the same , then

If a is not equal to b and difference between the roots of the equation x^2+ax+b=0 and x^2+bx+a=0 is the same , then

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Solution: Let alpha ,eta be the root of x^2+ax+b=0 andgamma ,delta be the root of x^2+bx+a=0

We are given

left | alpha -eta ight |=left | gamma -delta ight |\ \Rightarrow left | alpha -eta ight |^2=left | gamma -delta ight |^2\ \Rightarrow (alpha +eta )^2-4alpha eta =(gamma +delta )^2-4gamma delta \ \Rightarrow a^2-4b=b^2-4a\ \Rightarrow a^2-b^2+4(a-b)=0

\ Rightarrow (a-b)(a+b+4)=0\ \Rightarrow As ;a eq b,(a+b+4)=0

Posted by

Deependra Verma

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