,
A) There are exactly two distinct roots
B) There is one pair of equation real roots
C) There are three pairs of equal roots
D) Modulus of each root is 2
Correct Answer: C
Solution :
[c] \[\Delta =(1+x+{{x}^{2}})\left| \begin{matrix} 1 & 1 & 1 \\ {{x}^{2}} & 1 & x \\ x & {{x}^{3}} & 1 \\ \end{matrix} \right|=(1+x+{{x}^{2}}){{(x-1)}^{2}}\]Therefore, \[\Delta =0\]has roots 1, 1, \[{{\omega }^{{}}}\],\[{{\omega }^{{}}}\],\[{{\omega }^{2}}\],\[{{\omega }^{2}}\].
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