Marden's theorem states that if the three roots of a cubic polynomial are noncollinear points in the complex plane, then the two roots of the polynomial's derivative are the foci of the Steiner inellipse of the triangle whose vertices are the three original roots. This ellipse is tangent to the three sides at their midpoints.
Marden's Theorem
See also
Complex Plane, Cubic Polynomial, Derivative, Ellipse, Focus, Point, Polynomial Roots, Side, Steiner Inellipse, TangentExplore with Wolfram|Alpha
References
Marden, M. Geometry of Polynomials, 2nd ed. Providence, RI: American Mathematical Society, 1966.Cite this as:
Weisstein, Eric W. "Marden's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MardensTheorem.html