## Largest absolute value of a polynomial’s root [closed]

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 $$|x_0|<(n+1)c_{max}/|c_1|.$$

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.

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This question is inappropriate for MO. Please, check the FAQ for alternative places on the web where it might be posed. – Victor Protsak Aug 2 2010 at 6:02
Dokon, after your notation is fixed, so that $c-i$ becomes $c_i$, your problem is a homework problem. You can even prove a better upper bound $(\sum_{i=0}^n|c_i|)/|c_0|$ for all real roots of $c_0x^n+\dots+c_{n-1}x+c_n=0$. Vote to close (always for homeworks, check with the FAQ). – Wadim Zudilin Aug 2 2010 at 6:09
Dokon, try this en.wikipedia.org/wiki/…. For these elementary questions try e.g. en.wikipedia.org/wiki/Wikipedia:Reference_desk/… – Pietro Majer Aug 2 2010 at 7:26