# How the Roots of a Polynomial Depend on Its Constant Coefficient

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration shows how the roots (blue points) of the polynomial depend on the constant coefficient , which is shown enclosed in parentheses. The polynomial has multiple roots (cyan points) if and . The values of for roots of the second equation are called critical points (red points).

[more]
Contributed by: Izidor Hafner (May 2017)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

This Demonstration visualizes a part of the proof that equations of degree 5 are not solvable in radicals [1, pp. 77–90].

Reference

[1] D. Fuchs and S. Tabachnikov, *Mathematical Omnibus: Thirty Lectures on Classic Mathematics*, Providence: American Mathematical Society, 2007. www.math.psu.edu/tabachni/Books/taba.pdf.

## Permanent Citation