\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2014e.00582}
\itemau{Northshield, Sam}
\itemti{Geometry of cubic polynomials.}
\itemso{Math. Mag. 86, No. 2, 136-143 (2013).}
\itemab
Summary: Imagine a sphere with its equator inscribed in an equilateral triangle. This Saturn-like figure will help us understand from where Cardano's formula for finding the roots of a cubic polynomial $p(z)$ comes. It will also help us find a new proof of Marden's theorem, the surprising result that the roots of the derivative $p^{\prime}(z)$ are the foci of the ellipse inscribed in and tangent to the midpoints of the triangle determined by the roots of the polynomial.
\itemrv{~}
\itemcc{G75}
\itemut{Marden's theorem; cubic polynomials; ellipses; Cardano's formula}
\itemli{doi:10.4169/math.mag.86.2.136}
\end