Marden's Theorem
- Author:
- Erik Jacobsen
A demonstration of Marden's Theorem in the case that the roots form an isosceles triangle. Drag the right and top corners of the triangle (points A and C) along the axes.
A cubic polynomial has three roots which can be represented as three points in the complex plane. If the three points are not all along the same line, a triangle can be formed using the three points as vertices. Marden's theorem says that, in this case, the unique ellipse which is tangent to the midpoints of the three sides of the triangle has foci at the roots of the derivative of the polynomial.