Abstract
A method for determining the number of real quadratic factors of polynomials with real or complex coefficients is introduced. The method is based on formulating an equivalent problem of finding the number of real solutions of a certain algebraic system in two variables. Criteria for the existence of special quadratic factors are also introduced. The method consists of a finite algorithm realizable on a computer. It can be applied to determine the general decomposition structure of a given real polynomial. In particular the presence or absence of real or non-real roots can be ascertained.
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