Classical Formulas

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


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.


Quadratic Formula Extension Field Galois Theory Irreducible Polynomial Cube Root 
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  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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