Consider $(c_0, \ldots, c_{d-1}) \in \left(\mathbb{R}_{+}^{*}\right)^d$ and $P$ the polynomial $$X^d - c_{d-1} X^{d-1} - \cdots - c_1 X - c_0.$$ Show that the polynomial $P$ has a unique root in $\mathbb{R}_{+}^{*}$.
Consider $(c_0, \ldots, c_{d-1}) \in \left(\mathbb{R}_{+}^{*}\right)^d$ and $P$ the polynomial
$$X^d - c_{d-1} X^{d-1} - \cdots - c_1 X - c_0.$$
Show that the polynomial $P$ has a unique root in $\mathbb{R}_{+}^{*}$.