Post Closed as "too localized" by Victor Protsak, Wadim Zudilin, Robin Chapman, Yemon Choi, Andrey Rekalo
2 TeXed up

There is a polynomial c-1(x)^n $c_1 x^n + c-2(x)^(n-1) c_2 x^{n-1} +....+c-n(x)+c-(n+1) ....+c_n x+c_{n+1}$ with a root x=x0. $x=x_0$. If c-max $c_{max}$ is the largest absolute value of a c-i, $c_i$, show that

|x0|<(n+1)c-max/|c-1|$$|x_0|<(n+1)c_{max}/|c_1|.$$

Is this possible? I haven't seen any work on this on the net. Plus how do I keep it to (n+1), $(n+1)$, since if I take the x0 $x_0$ to the left there will be n terms on the right.

1

# Largest absolute value of a polynomial's root

There is a polynomial c-1(x)^n + c-2(x)^(n-1) +....+c-n(x)+c-(n+1) with a root x=x0. If c-max is the largest absolute value of a c-i, show that

|x0|<(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 x0 to the left there will be n terms on the right.