Consider the quadratic equation ax² + bx + c = 0, with a = 10^–10, b = –(10¹⁰ + 1)/10¹⁰, and c = 1. These are the coefficients of the expanded version of the polynomial p(x) = 10^–10(x–1)(x–10¹⁰), with the obvious roots x = 1 and x = 10¹⁰. Notice the behavior of the quadratic formula in the following command:

In [1]: import numpy as np
In [2]: a, b, c = 1.0e-10, -(1.0e10 + 1.)/1.0e10, 1.
In [3]: (-b - np.sqrt(b**2 - 4*a*c))/(2*a)
Out[3]: 1.00000000082740371