GeoGebra e o método de Briot & Bouquet para a resolução gráfica de equações cúbicas

• Autor(a) principal: Marques, Emília de Mendonça Rosa [UNESP]
• Data de Publicação: 2012
• Outros Autores: Souza, Aguinaldo Robinson de [UNESP]
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://revistas.pucsp.br/index.php/IGISP/article/view/8167; http://hdl.handle.net/11449/134917
• topic: Sequência didática; Parábola; Raízes reais de equações; Interpretação geométrica

In the mid-nineteenth century, french mathematicians Briot and Bouquet have proposed an intriguing graphical method for solving cubic equations "depressed" - the third degree equations that do not have the quadratic term. The proposal is simple geometric construction, though based on an ingenious algebra. We propose here the verification and testing graphical method through an instructional sequence using the software GeoGebra also present the ingenious algebraic development that resulted in this graphic method for determination of real roots of a cubic equation of the type x³ + px + q = 0 where p and q are real numbers. The method states that these solutions are summarized in the abscissas of the points of intersection of the circumference containing the origin and the center C (-q/2, 1-p/2) with the parable y = x².