casus irreducibilis
Let the polynomial
with complex coefficients be irreducible (http://planetmath.org/IrreduciblePolynomial2), i.e. irreducible in the field of its coefficients. If the equation can be solved algebraically (http://planetmath.org/AlgebraicallySolvable) and if all of its roots are real, then no root may be expressed with the numbers using mere real radicals (http://planetmath.org/NthRoot) unless the degree (http://planetmath.org/AlgebraicEquation) of the equation is an integer power (http://planetmath.org/GeneralAssociativity) of 2.
References
- 1 K. Väisälä: Lukuteorian ja korkeamman algebran alkeet. Tiedekirjasto No. 17. Kustannusosakeyhtiö Otava, Helsinki (1950).
Title | casus irreducibilis |
---|---|
Canonical name | CasusIrreducibilis |
Date of creation | 2013-03-22 15:21:00 |
Last modified on | 2013-03-22 15:21:00 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 12 |
Author | pahio (2872) |
Entry type | Theorem |
Classification | msc 12F10 |
Related topic | RadicalExtension |
Related topic | CardanosFormulae |
Related topic | TakingSquareRootAlgebraically |
Related topic | EulersDerivationOfTheQuarticFormula |