"If you change a polynomial's coefficients slightly, its roots will only change slight as well."

If only: http://en.wikipedia.org/wiki/Wilkinson's_polynomial

Section 3 "Roots are closely related to factoring a polynomial - for example, the roots of x2 - 4 are 2 and 2, and you can write x2 - 4 as (x-2)(x-2). We say that a root r has a multiplicity greater than one if (x-r) is a factor of the polynomial more than once." This is incorrect. x2 - 4 = (x - 2)(x + 2). Meaning the roots are 2 and -2. Also section 5, I'm not sure how you came up with those answers. The roots are 2 and -1. I tried the spreadsheet, but can't seem to get it to work.