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Suppose that $0 < a_0 \le a_1 \le \dots \le a_n$. Prove that the equation $$P(z) = a_0z^n + a_1z^{n-1} + \dots + a_{n-1}z + a_n = 0$$ has no root in the circle $|z| < 1$.

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    See also: http://math.stackexchange.com/q/188039/5363 for a related result.2012-09-08
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    $|z|<1$ is not a circle2013-05-07

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We want to show that $a_0z^n+\cdots+a_{n-1}z\neq -a_n$ for $|z|<1$. In fact, by induction we can prove something stronger: that $|a_0z^n+\cdots+a_{n-1}z|

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    I think $| a_0z^{n-1} + \cdots + a_{n-1} | < a_{n-1}$ might be wrong2012-09-08