Rovnice druhého stupňa v prostredí programu GeoGebra
Second Degree Equations in GeoGebra Environment
Abstract
GeoGebra is one of the most popular dynamical mathematical software that joins geometry, algebra and calculus. This tool help students to acquire knowledge about not only geometric objects. The relationships between the sum and product of the roots of a quadratic equation and the coefficients of the equation (Viete’s theorem) are considered. We give several geometrical (or graphical) methods of solving quadratic equations such as using the right triangle altitude theorem and the power of a point theorem. We will try to show some possibilities of the software GeoGebra to visualize these ways. In addition, we show that this can be solved by elementary geometry always using only ruler and compass.
- Keywords
- GeoGebra, quadratic equations, Vieta’s formula
- Classification
- H30, R20
References
Billich, M.: Solving Quadratic Equations. In: Proceedeings of the XIIth Czech-Polish-Slovak Mathematical School, Hluboš 2005, s. 88-92.
Čižmár, J.: Euklidovské konštrukcie. Proceedings of Seminars on Computational Geometry SCG’99, Volume 8, p. 31-47.
Kopka, J.: Ako riešiť matematické problémy. Ružomberok: VERBUM, 2010.
Kopka, J.: Hrozny problémů ve školské matematice. Ústí nad Labem, UJEP 1999.
Čižmár, J.: Euklidovské konštrukcie. Proceedings of Seminars on Computational Geometry SCG’99, Volume 8, p. 31-47.
Kopka, J.: Ako riešiť matematické problémy. Ružomberok: VERBUM, 2010.
Kopka, J.: Hrozny problémů ve školské matematice. Ústí nad Labem, UJEP 1999.