**Question P.** *Can a polynomial $\sum_{n=0}^ma_nx^n$ with coefficients $a_n\in\{-1,1\}$ have a multiple root in the interval $(\tfrac12,1)$?*

Also I am interested in a similar question for analytic functions.

**Question A.** *Let $f(x)=\sum_{n=0}^\infty a_nx^n$ a series with coefficients $a_n\in\{-1,1\}$ such that $\sup_{m\in\mathbb N}|\sum_{n=0}^ma_i|<\infty$. Can the analytic function $f$ have a multiple root in the interval $(0,1)$?*