Let $d \in \mathbb { N } ^ { * }$. Construct a map
$$\left\lvert \, \begin{aligned} r : \quad \mathbb { R } _ { d } [ X ] & \rightarrow \mathbb { R } \\ P & \mapsto r ( P ) \end{aligned} \right.$$
polynomial in the coefficients of $P$, such that, if $r ( P )$ is nonzero, then the roots of $P$ in $\mathbb { C }$ are simple.
\textit{Hint: You may use the previous question.}