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Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.

88 votes

Why do roots of polynomials tend to have absolute value close to 1?

I think the following geometric argument is interesting and maybe sufficient to answer "why" at an intuitive level (?). When we take the powers of $x$ in the complex plane, the absolute value scales g …
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