The roots of a polynomial vary smoothly as the coefficients vary. This is intuitively obvious. This is an important part of Abel's proof of the unsolvability of the quinitic. The probability of a random number being ambiguously real or complex has measure 0 (measure < epsilon, for all epsilon > 0), so you can ignore all computationally ambiguous cases. You don't need an exact calculation of any specific polynomial's root, to get the right answer of the measurement over all polynomials.