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!
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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; March 27th 2011 at 07:15 PM.
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