Determinants and Polynomial Root Structure
A little known property of determinants is developed in a manner accessible to beginning undergraduates in linear algebra. Using the language of matrix theory, a classical result by Sylvester that describes when two polynomials have a common root is recaptured. Among results concerning the structure of polynomial roots, polynomials with pairs of roots that are either multiplicative inverses or additive inverses are completely characterized.
© 2005 Taylor & Francis Group
L.G. de Pillis, "Determinants and Polynomial Root Structure", International Journal of Mathematical Education in Science and Technology, Vol. 36, No. 5, pp. 469-481, 15 July-15 August 2005.