Lucas-Gauss theorem

Complex polynomial roots, devirativeIn this Demonstration there are eight locators which represent the eight roots of the polynomial f(z)=(z-z1)(z-z2)…(z-z8). The convex hull of these roots is shown. Within, you see the roots of the derivative of f (and those of the higher derivatives).Applying the theorem to each derivative, you ultimately see a nested sequence of polygons: the convex hull of the roots of f, which contains the convex hull of the roots of f´, and so on. The relationship of the roots of a polynomial to the roots of its derivatives is complex, but is easily explored with this demonstrationComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic