I'm using Samuelson's result and a chapter from Marden's monograph "The Geometry of Polynomials". These are sophisticated results. Are these independent from the Jury-Cohn test to show that a polynomial has roots less than unity?

For expository reasons (to get a better understanding) I'd like to use the results for functions with real coefficients of second and third degree and find the restrictions on the coefficients. Is this a more difficult task than setting a polynomial $a_2 x^2 + a_1 x + a_0 = 0$ and manipulating coefficients such that the roots $\lambda_1$ and $\lambda_2$ are less than 1? Is there a result on this somewhere already? Thank you

exactlymodulus one, and then perturbations should should which direction the inequality would move? $\endgroup$ – Jared Jul 2 '13 at 22:02