TY - JOUR
T1 - A systematic approach to the exact roots of polynomials
AU - Beji, Serdar
PY - 2008/6
Y1 - 2008/6
N2 - A unified framework is introduced for obtaining the exact roots of a polynomial by establishing a corresponding polynomial of one degree less. The approach gives the well-known solutions for the second and third degree polynomials and a new solution for the quartic equation, which is different in form from the classical Ferrari-Cardan solution. In accord with Abel's proof, the method produces no solution for the quintic equation.
AB - A unified framework is introduced for obtaining the exact roots of a polynomial by establishing a corresponding polynomial of one degree less. The approach gives the well-known solutions for the second and third degree polynomials and a new solution for the quartic equation, which is different in form from the classical Ferrari-Cardan solution. In accord with Abel's proof, the method produces no solution for the quintic equation.
KW - Cardan and Cardan-Ferrari Solutions
KW - Systematic approach
KW - Zeros of the second, third, and fourth degree polynomials
UR - http://www.scopus.com/inward/record.url?scp=50949118835&partnerID=8YFLogxK
U2 - 10.1007/s00009-008-0141-6
DO - 10.1007/s00009-008-0141-6
M3 - Article
AN - SCOPUS:50949118835
SN - 1660-5446
VL - 5
SP - 163
EP - 172
JO - Mediterranean Journal of Mathematics
JF - Mediterranean Journal of Mathematics
IS - 2
ER -