Professional paper

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

Luka Marohnić ; Tehničko veleučilište u Zagrebu, Zagreb
Bojan Kovačić ; Tehničko veleučilište u Zagrebu, Zagreb
Bojan Radišić ; Veleučilište u Požegi, Požega

Abstract

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 possible approximation for the numbers~$\varphi_n$ is given.

Keywords

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

Hrčak ID:

135202

URI

https://hrcak.srce.hr/135202

Publication date:

2.3.2015.

Article data in other languages: croatian

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