A) 3
B) \[3,\,\,3i,\,3{{i}^{2}}\]
C) \[3,\,3\omega ,\,3{{\omega }^{2}}\]
D) None of these
Correct Answer: C
Solution :
Let \[x={{27}^{1/3}}\] \[={{x}^{3}}-27=0\] Þ \[(x-3)({{x}^{2}}+3x+9)=0\] \[x=3,x=3\left( \frac{-1\pm i\sqrt{3}}{2} \right)\]. Hence, roots are\[3,\,3\omega ,3{{\omega }^{2}}\]. Trick: As we know \[{{(27)}^{1/3}}\] must have 3 roots, so (a) option cannot be the best. Here (c) satisfies.
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