A) \[{{x}^{2}}-6x+1=0\]
B) \[{{x}^{2}}-x+6=0\]
C) \[6{{x}^{2}}+x+1=0\]
D) \[{{x}^{2}}+x-6=0\]
Correct Answer: D
Solution :
Let the roots be \[\alpha \] and \[\beta \]. Then, \[\alpha +\beta =-1\] (given) and \[\frac{1}{\alpha }+\frac{1}{\beta }=\frac{1}{6}\] \[\Rightarrow \] \[\frac{\beta +\alpha }{\alpha \beta }=\frac{1}{6}\] \[\therefore \] \[-\frac{1}{\alpha \beta }=\frac{1}{6}\] \[\Rightarrow \] \[\alpha \beta =-6\] So, the required equation is \[{{x}^{2}}+x-6=0\]
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