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- Jan 26, 2012

- 4,198

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If $a_0\ge a_1 \ge a_2\ge \cdots\ge a_n\ge 0,$ prove that any root $r$ of the polynomial

$$P(z)\equiv a_0 z^n+a_1 z^{n-1}+\cdots+a_n$$

satisfies $|r|\le 1$; i.e., all the roots lie inside or on the unit circle centered at the origin in the complex plane.

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