KoG, Vol. 5. No. 5., 2000.
Izvorni znanstveni članak
The Consequences of Descartes's Method for Factorization of 4th Degree Polynomial
Radimir Viher
; Građevinski fakultet Sveučilišta u Zagrebu, Zagreb, Hrvatska
Sažetak
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).
Ključne riječi
Descartes's method; factorization; cubic resolvent; types of roots; characterizations of types of roots; plane quartic curves
Hrčak ID:
4001
URI
Datum izdavanja:
19.2.2002.
Posjeta: 1.647 *