Answer by Peter Taylor for Multiple roots of polynomials with coefficients...
Question P.Can a polynomial $P(x)=\sum_{n=0}^ma_nx^n$ with coefficients $a_n\in\{-1,1\}$ (and $P(1)=0$) have a multiple root in the interval $(\tfrac12,1)$?Yes. The following four Littlewood...
View ArticleAnswer by მამუკაჯიბლაძე for Multiple roots of polynomials with coefficients...
Not an answer, only some sort of evidence for A, hence community wiki.There seems to be an algorithm that produces a sequence of polynomials $(P_n)$ like in P, with $P_0=1$, $P_{n+1}=P_n\pm x^{n+1}$,...
View ArticleMultiple roots of polynomials with coefficients $\pm 1$
Question P.Can a polynomial $P(x)=\sum_{n=0}^ma_nx^n$ with coefficients $a_n\in\{-1,1\}$ (and $P(1)=0$) have a multiple root in the interval $(\tfrac12,1)$?Also I am interested in a similar question...
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