If $x,y,z$ are all distinct and $\begin{vmatrix}x&x^2&1+x^3\\y&y^2&1+y^3\\z&z^2&1+z^3\end{vmatrix}=0$ then the value of $xyz$ is

Question

$(a)\;-2\qquad(b)\;-1\qquad(c)\;-3\qquad(d)\;None\;of\;these$