A) 1
B) \[-4\]
C) 4
D) 2
E) \[-2\]
Correct Answer: B
Solution :
Given, \[f(\alpha )=\left| \begin{matrix} 1 & \alpha & {{\alpha }^{2}} \\ \alpha & {{\alpha }^{2}} & 1 \\ {{\alpha }^{2}} & 1 & \alpha \\ \end{matrix} \right|\] \[=1({{\alpha }^{3}}-1)-\alpha ({{\alpha }^{2}}-{{\alpha }^{2}})+{{\alpha }^{2}}(\alpha -{{\alpha }^{4}})\] \[={{\alpha }^{3}}-1-0+{{\alpha }^{3}}-{{\alpha }^{6}}\] \[\Rightarrow \]\[f(\sqrt[3]{3})=3-1-0+3-{{3}^{2}}=6-10=-4\]You need to login to perform this action.
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