  The theory of polar forms of polynomials is used to provide for sharp bounds
on the radius of the largest possible disc (absolute stability radius), and on
the length of the largest possible real interval (parabolic stability radius),
to be inscribed in the stability region of an explicit Runge-Kutta method. The
bounds on the absolute stability radius are derived as a consequence of Walsh's
coincidence theorem, while the bounds on the parabolic stability radius are
achieved by using Lubinsky-Ziegler's inequality on the coefficients of
polynomials expressed in the Bernstein bases and by appealing to a generalized
variation diminishing property of Bezier curves. We also derive inequalities
between the absolute stability radii of methods with different orders and
number of stages.
