A) \[\frac{{{n}^{2}}\left( {{l}^{2}}-{{m}^{2}} \right)}{{{l}^{2}}\left( {{m}^{2}}-{{n}^{2}} \right)},l\]
B) \[\frac{-{{m}^{2}}\left( {{l}^{2}}-{{m}^{2}}+{{n}^{2}} \right)}{{{l}^{2}}\left( {{m}^{2}}-{{n}^{2}} \right)},\frac{1}{2}\]
C) \[\frac{{{n}^{2}}\left( {{l}^{2}}+{{m}^{2}}+{{n}^{2}} \right)}{{{m}^{2}}\left( {{m}^{2}}-{{n}^{2}} \right)},1\]
D) \[\frac{-{{m}^{2}}\left( {{l}^{2}}+{{n}^{2}} \right)}{mn\left( {{m}^{2}}-{{n}^{2}} \right)},\frac{1}{2}\]
Correct Answer: A
Solution :
(a): In the equation \[a{{x}^{2}}+bx+c=0\] when \[a+b+c=0\], then the roots are 1 and \[\frac{c}{a}\]. Use the following justification and compare: here,\[a={{l}^{2}}\left( {{m}^{2}}-{{n}^{2}} \right);b={{m}^{2}}\left( {{n}^{2}}-{{l}^{2}} \right)\]and \[c={{n}^{2}}\left( {{l}^{2}}-{{m}^{2}} \right)\]
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