For finding all the roots, the oldest method is, when a root has been found, to divide the polynomial by , and restart iteratively the search of a root of the quotient polynomial. However, except for low degrees, this does not work well because of the numerical instability: Wilkinson's polynomial shows that a very small modification of one coefficient may change dramatically not only the value of the roots, but also their nature (real or complex). Also, even with a good approximation, when one evaluates a polynomial at an approximate root, one may get a result that is far to be close to zero. For example, if a polynomial of degree 20 (the degree of Wilkinson's polynomial) has a root close to 10, the derivative of the polynomial at the root may be of the order of formula_2 this implies that an error of formula_3 on the value of the root may produce a value of the polynomial at the approximate root that is of the order of formula_4