Wilkinson's polynomial | Dependence of roots on coefficients

Wilkinson's polynomial | Dependence of roots on coefficients

If you change the coefficients of a polynomial a little bit, do you change the location of its zeros a little bit? In other words, do the roots of a polynomial depend continuously on its coefficients? You would think so, and you’d be right. Sorta. It’s easy to see that small change to a coefficient could result in a qualitative change, such as a double root splitting into two distinct roots close together, or a real root acquiring a small imagin…