most recent 30 from http://mathoverflow.net 2013-06-18T05:15:05Z http://mathoverflow.net/feeds/question/34210 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/34210/largest-absolute-value-of-a-polynomials-root Dokon 2010-08-02T05:37:49Z 2010-08-02T07:37:33Z

<p>There is a polynomial $c_1 x^n + c_2 x^{n-1} +....+c_n x+c_{n+1}$ with a root $x=x_0$. If $c_{max}$ is the largest absolute value of a $c_i$, show that $$|x_0|&lt;(n+1)c_{max}/|c_1|.$$</p> <p>Is this possible? I haven't seen any work on this on the net. Plus how do I keep it to $(n+1)$, since if I take the $x_0$ to the left there will be n terms on the right.</p>