IJPAM: Volume 16, No. 2 (2004)

APPLICATION OF A TSCHIRNHAUSIAN
TRANSFORM TO QUARTIC EQUATIONS

Yoshihiro Mochimaru
Department of International Development Engineering
Graduate School of Science and Engineering
Tokyo Institute of Technology
2-12-1, O-okayama, Meguru-ku
Tokyo 152-8550, JAPAN
e-mail: ymochima@o.cc.titech.ac.jp


Abstract.Tschirnhausian transform of a quadratic polynomial type is applied to quartic equations to obtain all roots algebraically. The subsidiary equation for a parameter is given as a cubic equation explicitly in terms of coefficients of the said quartic equation, with an exception that the quartic becomes a compound quadratic in a parallel shift.

Received: July 14, 2004

AMS Subject Classification: 11D25

Key Words and Phrases: Tschirnhausian transform, quartic equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 16
Issue: 2