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Classical Formulas

  • Joseph Rotman
Part of the Universitext book series (UTX)

Abstract

Let us now derive the classical formulas for the roots of quadratics, cubics, and quartics. Consider the quadratic equation
$$ {X^2}{\text{ + bX + }}c{ = }0 $$
Replacing X by x = X - b/2, this equation becomes
$$ {x^2}{ + }c{ - }{b_2}{/}4{ = }0 $$
it follows that \( x{ = }\pm \frac{1}{2}\sqrt {{{b^2}{ - }4c}} \). Of course, one obtains the usual formula by replacing x by X + b/2.

Keywords

Quadratic Formula Extension Field Galois Theory Irreducible Polynomial Cube Root 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literatur

  1. 2.
    R.P. Feynman, “What do you care what other people think?” Further adventures of a curious character, Bantam, 1988, page 95.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Joseph Rotman
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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