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  • If the sum of the roots of the equation ax^2+bx+c=0 is equal to the sum of their Squares ,then a, b, anc c satisfy

If the sum of the roots of the equation ax^2+bx+c=0 is equal to the sum of their Squares ,then a, b, anc c satisfy

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Solution:  

\ alpha +eta =-b/a\ \Rightarrow alpha imes eta =c/a

Given that  

\Rightarrow alpha +eta = alpha ^2+ eta ^2=-b/a\ \Rightarrow b^2/a^2=(alpha +eta )^2=alpha ^2+eta ^2+2alpha imes eta =-b/a+2c/a

\Rightarrow -ab+2ca=b^2

Posted by

Deependra Verma

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