A) \[\pm \omega \]
B) \[\pm {{\omega }^{2}}\]
C) \[\pm \omega ,\,\pm {{\omega }^{2}}\]
D) None of these
Correct Answer: C
Solution :
\[{{x}^{12}}-1=({{x}^{6}}+1)({{x}^{6}}-1)=({{x}^{6}}+1)({{x}^{2}}-1)({{x}^{4}}+{{x}^{2}}+1)\] Common roots are given by \[{{x}^{4}}+{{x}^{2}}+1=0\] \[\therefore \,\,\,\]\[{{x}^{2}}=\frac{-1\pm i\sqrt{3}}{2}=\omega ,{{\omega }^{2}}\]or \[{{\omega }^{4}},{{\omega }^{2}}\] \[(\because {{\omega }^{3}}=1)\] or \[x=\pm {{\omega }^{2}},\pm \omega \]
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