On the bottom of the page where this exercise is from (D. Lay, Linear Algebra and its applications, p. 186) it is written:
Exercises 9 and 10 concern determinants of the following Vandermonde matrices: \[ V(t) = \begin{pmatrix} 1 & t & t^2 & t^3 \\ 1 & x_1 & x_1^2 & x_1^3\\ 1 & x_2 & x_2^2 & x_2^3 \\ 1 & x_3 & x_3^2 & x_3^3 \end{pmatrix} \]
(Remark: and another one which is not important for the exercise above). The exercise above is No. 10:
10. Let $f(t) = \det V$, with $x_1$, $x_2$, $x_3$ all distinct. Explain why $f(t)$ is a cubic polynomial, show that the coefficient of $t^3$ is nonzero, and find 3 points on the graph of $f$.
I dont't know if this qualifies as an answer, but it's too long for a comment.