Os caminhos das raízes da função quadrática - molde, modelo e estilo

By fixing two real coefficients and varying the remaining realcoefficient of the quadratic function, the model of the pathsdescribed by the two roots of the function in the complex planeis obtained (Yamaoka (2023)). A style is a set of models thatare related to each other and share the same mold -structure-(except the style 4 originating from 𝑓𝑎 (𝑧) = 𝑎𝑧^2, 𝑎 ∈ R∗, consistingof a single model). We determine the number of connectedcomponents of the path of each root per model. We determinethe connected components of each mold. We give examples ofthe molds. We discuss the continuity and differentiability of thetwo roots: they are continuous in their domains and the simpleroots are infinitely differentiable (with the exception of the infinitelydifferentiable zero double root of 𝑓𝑎 (𝑧) = 𝑎𝑧^2, 𝑎 ∈ R∗,the other double roots that appear in the text are not differentiable).The theoretical foundation that supports the resultsobtained here belongs to Classical Analysis.