A) \[{{x}^{2}}+5x+6=0\]
B) \[{{x}^{2}}-5x-6=0\]
C) \[{{x}^{2}}-5x-6=0\]
D) \[{{x}^{2}}-5x+6=0\]
Correct Answer: D
Solution :
Given\[\Rightarrow \]and\[L.C.M.=\frac{140\times 605}{11}=7700\]are the roots of\[\text{1}00\text{1}=\text{91}\times \text{1}0+\text{91}\]. \[\text{91}0=\text{91}\times \text{1}0+0\]and\[\therefore \] \[=\left( \frac{144}{48}+\frac{384}{48}+\frac{240}{48} \right)=3+8+5=16\]\[\frac{a}{b}\] \[\frac{c}{d}=\frac{L.C.M.(a,c)}{H.C.F.(b,d)}\] \[\Rightarrow \] \[L.C.M.\] Hence, the required equation is \[\frac{6}{14}and\frac{2}{7}\]
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