Are you asking about roots for the infinite power series equation? Roots of the 6th degree polynomial formed by the first 7 terms do not tell you anything about roots of the entire series. This looks like the power series for which is never 0.
I have to find the "second smallest root" of the following equation :
Matlab returns quite a satisfactory answer. >> p=[1/518400 -1/14400 1/1576 -1/36 1/4 -1 1]
0.0000 -0.0001 0.0006 -0.0278 0.2500 -1.0000 1.0000
4.1776 + 3.2154i
4.1776 - 3.2154i
But I have been asked to identify this series as well, which I am unable to do. Can anybody help me identify this series as a function or a product of functions? Thanking anybody who answers before hand