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If a , b , c are unequal , what is the...

If a , b , c are unequal , what is the condition that value of the following determinant is zero ?
`Delta=|(a,a^2,a^3+1),(b,b^2,b^3+1),(c,c^2,c^3+1)|`

A

`1+abc=0`

B

`a+b+c+1=0`

C

`(a-b)(b-c)(c-a)=0`

D

None of these

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The correct Answer is:
A
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