On real roots of polynomials $x^n-x-1$

Osječki matematički list

Kovačić, Bojan²  Marohnić, Luka²  Radišić, Bojan¹ 

[1] Veleučilište u Požegi, Požega;Tehničko veleučilište u Zagrebu, Zagreb

关键词: polynomial;    root;    sequence;    golden ratio;    plastic number;    approximation;    Newton';    s method;   

DOI  :  

学科分类：社会科学、人文和艺术（综合）

来源: Sveuciliste Josipa Jurja Strossmayera u Osijeku * Odjel za Matematiku / University of Osijek, Department of Mathematics

【 摘 要 】

In this paper, it is first shown that for every natural number $n\geq 2$ the polynomial $\pi_n(x)=x^n-x-1$ has a unique positive root~$\varphi_n$. Then some properties of the sequence~$\left(\varphi_n\right)_{n\geq 2}$ are proved and a...

【 授权许可】

Unknown