Re:Why do roots of polynomials tend to have absolute value 1?
by lacker on Sunday October 05, 2014 @05:33AM
(#8411864)
This seems intuitive without needing complex formulas. If you have a big polynomial with, say, one term of ax^300 and one term of b, anything where there is a solution, these terms will tend to be roughly the same order of magnitude. If you are generating polynomials in such a way where a and b are roughly the same order of magnitude, then x^300 and 1 will have to have roughly the same order of magnitude. This only happens when |x| is pretty close to 1.
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Re:Why do roots of polynomials tend to have absolute value 1?
by conistonwater on Sunday October 05, 2014 @07:50AM
(#8412052)
This is the heuristic explanation given in the answer just below the top one, so you are definitely right there.
I also think it's important to mention that the roots ax^300-b have magnitude (b/a)^(1/300), which is much closer to 1 than b/a, which is why the magnitudes of a and b don't matter very much.