Portal de Periódicos da CAPES

Determinantes de Hurwitz para verificar quando polinômios possuem somente raízes reais

2023; Sociedade Brasileira de Matemática; Volume: 11; Issue: 24 Linguagem: Inglês

10.21711/2319023x2023/pmo1124

2319-023X

Fábio Lucas Rodrigues, Oyran Raizzaro,

Mathematics and Applications

When it comes to polynomial equations, the mathematician Sridhara in the twelfth century determined the current formula for solving quadratic equations, known as Bhas kara.In 1545 Girolamo Cardano published the method for solving equations of the third and fourth degree currently known as the Cardano-Tartaglia method.But it was the French mathematician E. Galois who, upon completing Abel's work, showed that a solution by radicals for polynomial equations of degree greater than four is not possible.Based on the above context, it is easy to know if a polynomial of degree less than or equal to four has only real roots, in this way, using the Hurwitz Matrices, we will approach the method that verifies when a polynomial of any degree has only real roots and confront this method with the solutions by radicals of the equations of degree: two, three and the biquadratic equation.