Marden's theorem

A triangle and its Steiner inellipse. The zeroes of p(z) are the black dots, and the zeroes of p'(z) are the red dots). The center green dot is the zero of p"(z). Marden's theorem states that the red dots are the foci of the ellipse.

In mathematics, Marden's theorem, named after Morris Marden but proved about 100 years earlier by Jörg Siebeck, gives a geometric relationship between the zeroes of a third-degree polynomial with complex coefficients and the zeroes of its derivative. See also geometrical properties of polynomial roots.