Prove that if the absolute value of the coefficients of a complex polynomial with a leading coefficient of 1 is maximum 1, than the absolute values of its roots are smaller than 2.
Any help would be appreciated!
Follow Math Help Forum on Facebook and Google+
This result is proved using the triangle inequality:
Let be the monic polynomial and a root. Then,
The result follows quickly from this.
Last edited by ojones; Mar 27th 2011 at 08:15 PM.
View Tag Cloud