The plastic number and its generalized polynomial

The polynomial $X^3-X-1$ has a unique positive root known as plastic number, which is denoted by $\rho$ and is approximately equal to $1.32471795$. In this note we study the zeroes of the generalized polynomial $X^k-{\sum }_{j=0}^{k-2}{X}^j$ for $k\ge 3$ and prove that its unique positive root ${\lambda }_k$ tends to the golden ratio $\varphi =\frac{1+\sqrt{5}}{2}$ as $k \to \infty$\mathrm{.}Wealsoderiveboundson$\lambda_{k}$ in terms of Fibonacci numbers.