A) \[mn{{x}^{2}}+(m+n-2mn)x+mn-m-n+1=0\]
B) \[mn{{x}^{2}}-(2mn+m+n)x+mn+m+mn+1=0\]
C) \[mn{{x}^{2}}+(2mn+m+n)x+mn+m+n+1=0\]
D) \[mn{{x}^{2}}-(2mn-m-n)x+mn-m-n+1=0\]
Correct Answer: D
Solution :
[d] \[m=\sum\limits_{r=0}^{\infty }{{{a}^{r}}}=\frac{1}{1-a}\Rightarrow a=\frac{m-1}{m}\] Similarly, \[b=\frac{n-1}{n}\] Equation having roots a and b is: \[{{x}^{2}}-(a+b)x+ab=0\] or \[{{x}^{2}}-\left( \frac{m-1}{m}+\frac{n-1}{n} \right)x+\frac{(m-1)\,(n-1)}{mn}=0\] or \[mn{{x}^{2}}-(2mn-m-n)x+mn-m-n+1=0\]You need to login to perform this action.
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