question_answer

If a, b and c are positive numbers in a G.P., then the roots of the quadratic equation \[({{\log }_{e}}a){{x}^{2}}-2({{\log }_{e}}b)x+({{\log }_{e}}c)=0\] are ______.

A)  \[-1\,\,and\,\,{{\log }_{c}}a\]     

B)  \[-1\,\,and\,\,{{\log }_{a}}c\]

C)  \[1\,\,and\,\,{{\log }_{c}}a\]                  

D)  \[1\,\,and\,\,{{\log }_{a}}c\]

E)  None of these