Exact and approximate solutions to the minimum of $1+x+\cdots +x^{2n}$

Aaron Hendrickson, Claude F. Leibovici

The polynomial $f_{2n}(x)=1+x+\cdots +x^{2n}$ and its minimizer on the real line $x_{2n}=\mathrm{arginf}{f}_{2n}(x)$ for $n\in \mathbb{N}$ are studied. Results show that $x_{2n}$…