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 $|z| < 1$.
Prove the equation has no root in the circle $|z| < 1$
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complex-analysis
complex-numbers
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2See also: http://math.stackexchange.com/q/188039/5363 for a related result. – 2012-09-08
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0$|z|<1$ is not a circle – 2013-05-07