Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2017-01-10T14:58:57Z No. of bitstreams: 2 Dissertação - Pollyana Gomes Volpato - 2016.pdf: 1172027 bytes, checksum: 6e8ebfc67549380e690db90bc68b9104 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-01-11T09:42:09Z (GMT) No. of bitstreams: 2 Dissertação - Pollyana Gomes Volpato - 2016.pdf: 1172027 bytes, checksum: 6e8ebfc67549380e690db90bc68b9104 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-01-11T09:42:09Z (GMT). No. of bitstreams: 2 Dissertação - Pollyana Gomes Volpato - 2016.pdf: 1172027 bytes, checksum: 6e8ebfc67549380e690db90bc68b9104 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-12-09 / The main objective of this work is to demonstrate Marden’s Theorem, which tells us that given a third-degree polynomial with complex coefficients, the roots of this polynomial are not collinear and form a triangle T in the complex plane. There is a unique ellipse inscribed in T and tangent to the sides at their midpoints. The foci of this ellipse are the roots of the derivative of the polynomial. We show that such an ellipse is Steiner’s Ellipse. We make a generalization of the Marden Theorem using degree n polynomial. / Temos como objetivo central neste trabalho demonstrar o Teorema de Marden, que nos diz que, dado um polinômio de terceiro grau com coeficientes complexos, as raízes desse polinômio não são colineares e formam um triângulo T no plano complexo. Há uma única elipse inscrita em T e tangente aos lados nos seus pontos médios. Os focos dessa elipse são as raízes da derivada do polinômio. Mostramos que tal elipse é a Elipse de Steiner. Fazemos uma generalização do Teorema de Marden utilizando polinômio de grau n.