if \(a,b,c\) are unequal what is the condition that the value of following determinat is zero \(...

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if \(a,b,c\) are unequal what is the condition that the value of following determinat is zero \(\delta=\left| \begin{matrix} a & { a }^{ 2 } & { a }^{ 3 }+1 \\ b & b^{ 2 } & b^{ 3 }+1 \\ c & c^{ 2 } & c^{ 3 }+1 \end{matrix} \right| \)
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