question_answer

If \[\alpha ,\beta ,\gamma \] are the roots of \[{{x}^{3}}-3{{x}^{2}}+3x+7=0\] (\[\omega \] is the cube root of unity), then\[\frac{\alpha -1}{\beta -1}+\frac{\beta -1}{\gamma -1}\]\[+\frac{\gamma -1}{\alpha -1}\] is

A)  \[\frac{3}{\omega }\]                

B)  \[{{\omega }^{2}}\]

C)  \[2{{\omega }^{2}}\]          

D)  \[3{{\omega }^{2}}\]