Abstract
We see in this chapter how Galois theory can be used to get a satisfactory answer to the problem of constructions with ruler and compass. By analogous methods, we discuss the problem of solving polynomial equations using radicals and we show how Galois theory allows us to understand the explicit resolution of equations of degrees up to 4. Finally, we will study the behavior of the Galois group of an equation when we vary the coefficients.
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© 2005 Springer Science+Business Media, Inc.
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(2005). Applications. In: A Field Guide to Algebra. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/0-387-26955-X_5
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DOI: https://doi.org/10.1007/0-387-26955-X_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-21428-3
Online ISBN: 978-0-387-26955-9
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