casus irreducibilis

Let the polynomialPlanetmathPlanetmath


with complex coefficients aj be irreducible (, i.e. irreducible in the field (a1,,an)  of its coefficients.  If the equation  P(x)=0  can be solved algebraically ( and if all of its roots are real, then no root may be expressed with the numbers aj using mere real radicalsPlanetmathPlanetmathPlanetmathPlanetmath ( unless the degree ( n of the equation is an integer power ( of 2.


  • 1 K. Väisälä: Lukuteorian ja korkeamman algebran alkeet.  Tiedekirjasto No. 17. Kustannusosakeyhtiö Otava, Helsinki (1950).
Title casus irreducibilisMathworldPlanetmath
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