Question:medium
If \( a, b \) and \( c \) are distinct reals and the determinant
\[
\begin{vmatrix}
a^3+1 & a^2 & a \\
b^3+1 & b^2 & b \\
c^3+1 & c^2 & c
\end{vmatrix} = 0,
\]
then the product \( abc \) is
If \( a, b \) and \( c \) are distinct reals and the determinant
\[
\begin{vmatrix}
a^3+1 & a^2 & a \\
b^3+1 & b^2 & b \\
c^3+1 & c^2 & c
\end{vmatrix} = 0,
\]
then the product \( abc \) is
Show Hint
When variables are distinct, Vandermonde determinant is non-zero, so focus on the remaining factor.
Updated On: Apr 30, 2026
- \( -1 \)
- \( 0 \)
- \( 1 \)
- \( 2 \)
- \( 3 \)
Show Solution
The Correct Option is A
Solution and Explanation
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