If \[a,b,c\]are unequal what is the condition that the value of the following determinant is zero \[\Delta =\left| \,\begin{matrix} a & {{a}^{2}} & {{a}^{3}}+1 \\ b & {{b}^{2}} & {{b}^{3}}+1 \\ c & {{c}^{2}} & {{c}^{3}}+1 \\ \end{matrix}\, \right|\] [IIT 1985; DCE 1999]

If \[a,b,c\]are unequal what is the condition that the value of the fo

1.	If \[a,b,c\]are unequal what is the condition that the value of the following determinant is zero \[\Delta =\left\| \,\begin{matrix} a & {{a}^{2}} & {{a}^{3}}+1 \\ b & {{b}^{2}} & {{b}^{3}}+1 \\ c & {{c}^{2}} & {{c}^{3}}+1 \\ \end{matrix}\, \right\|\] [IIT 1985; DCE 1999]
A.	\[1+abc=0\]
B.	\[a+b+c+1=0\]
C.	\[(a-b)(b-c)(c-a)=0\]
D.	None of these
Answer» B. \[a+b+c+1=0\]

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If \[a,b,c\]are unequal what is the condition that the value of the following determinant is zero \[\Delta =\left| \,\begin{matrix} a & {{a}^{2}} & {{a}^{3}}+1 \\ b & {{b}^{2}} & {{b}^{3}}+1 \\ c & {{c}^{2}} & {{c}^{3}}+1 \\ \end{matrix}\, \right|\] [IIT 1985; DCE 1999]

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