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

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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).

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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.