A) \[f(\alpha )+f(\beta )+f(\lambda )\]
B) \[f(\alpha )f(\beta )+f(\beta )f(\lambda )+f(\gamma )+f(\alpha )\]
C) \[f(\alpha )f(\beta )f(\gamma )\]
D) \[-f(\alpha )f(\beta )f(\gamma )\]
Correct Answer: D
Solution :
[d] \[\left| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \\ \end{matrix} \right|=-({{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc)\] \[=-(a+b+c)(a+b{{\omega }^{2}}+c\omega )(a+b\omega +c{{\omega }^{2}})\] \[=-f(\alpha )f(\beta )f(\lambda )[\because \,\alpha =1,\,\beta =\omega ,={{\omega }^{2}}]\]
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