AN APPROACH TO THE STUDY OF THE QUADRATIC FUNCTION USING THE ALGEBRAIC FORM OF A COMPLEX NUMBER

Resumen

This article aims to present a new method for calculating the roots of a quadratic function, also called polynomial function of the 2nd degree, without resorting to formulas known in the literature in Mathematics. In this sense, the complex number is used in the algebraic form x=m+ni. In the application session, some problems are addressed, including in the area of Physics, in which the calculation of roots is compared, considering the development from known expressions, and compared with the method presented in this work in order to validate what was proposed. It was found that the method, presented in the form of a theorem, does not have the need to apply the known formulas, because the mathematical development leads to solving only a linear system with two variables m and n, for example, in which m will represent the abscissa of the vertex of the parabola of the given function and n can be written as an expression that involves the discriminant ∆. In addition, a discussion of the nature of the roots of the quadratic function is made from the analysis of the parameter n, which will indicate whether they are real or complex. It was concluded that, considering the complex number in the form x=m+ni, the method presented is of simple applicability and great relevance.