A) \[\frac{a+b}{a-b}\]
B) \[\frac{a-b}{a+b}\]
C) 0
D) None of these
Correct Answer: B
Solution :
\[\frac{{{x}^{2}}-bx}{ax-c}=\frac{\lambda -1}{\lambda +1}\] \[\Rightarrow \] \[({{x}^{2}}-bx)(\lambda +1)=(ax-c)(\lambda -1)\] \[\Rightarrow \] \[{{x}^{2}}(\lambda +1)-bx(\lambda +1)-ax(\lambda -1)\] \[+c(\lambda -1)=0\] \[\Rightarrow \] \[{{x}^{2}}(\lambda +1)-x[b(\lambda +1)+a(\lambda -1)]\] \[+x(\lambda -1)=0\] Since, roots of the equation are equal and opposite, therefore sum of the roots must be equal to zero. \[\therefore \] \[\frac{b(\lambda +1)+a(\lambda -1)}{\lambda +1}=0\] \[\Rightarrow \] \[b\lambda +b+a\lambda -a=0\] \[\Rightarrow \] \[\lambda (b+a)=a-b\] \[\Rightarrow \] \[\lambda =\frac{a-b}{a+b}\]
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