# 2014-17 Zeros of a polynomial

Let $p(x)=x^n+x^{n-1}+a_{n-2}x^{n-2}+\cdots+a_1 x_1 + a_0$ be a polynomial. Prove that if $$p(z)=0$$ for a complex number $$z$$, then $|z| \le 1+ \sqrt{\max (|a_0|,|a_1|,|a_2|,\ldots,|a_{n-2}|)}.$

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