KoG, Vol. 5. No. 5., 2000.
Original scientific paper
The Consequences of Descartes's Method for Factorization of 4th Degree Polynomial
Radimir Viher
; Faculty of Civil Engineering, University of Zagreb, Zagreb, Croatia
Abstract
In this article we give in details description of Descartes's method for factorization of the fourth degree polynomial (over the field R) in the following reduced form P_4(x) = x_4+a_2x^2+a_1x+a_0 = (x^2+Ax+B)(x^2+Cx+D). When we seek the solution for A we get the following cubic resolvent P_3(t) = t^3+2a_2t^2+({a_2}^2-4a_0)t-{a_1}^2, where t = A^2. At the end, we formulate and prove two theorems. In the first one, we find the correspondences between the types of the roots of P_3(t) and P_4(x) while in the second one, we give the characterizations of types of roots for P_3(t).
Keywords
Descartes's method; factorization; cubic resolvent; types of roots; characterizations of types of roots; plane quartic curves
Hrčak ID:
4001
URI
Publication date:
19.2.2002.
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