Introduction

Lill's method is a dynamic process that allows you to visualize the real zeros, if any, of any polynomial of positive degree in a real variable. With this method, we can test for the existence of these zeros and analyze how they vary with the coefficients of the polynomial. The method also has the advantage of being easy to implement on a computer and adaptable to an interactive approach, such as the one presented here.

Let's consider a polynomial equation in the real variable \(x\) \[(1) a_n x^n + a_{n-1}x^{n-1} + \ldots + a_1 x + a_0 = 0\] with real coefficients \(a_n,\cdots,a_0\), where \(n\) is a positive integer and \(a_n \neq 0\).

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This text is a slightly modified version of the following article (in Portuguese) published by Atractor in Gazeta de Matemática


(*) Difficulty level: University