ABSTRACT
A special problem associated with polynomials Pn(x) is the possibility of complex roots. Newton's method, the secant method, and Muller's method all can find complex roots if complex arithmetic is used and complex initial approximations are specified. Fortunately, complex arithmetic is available in several programming languages, such as FORTRAN. However, hand calculation using complex arithmetic is tedious and time consuming. When polynomials with real coefficients have complex roots, they occur in conjugate pairs, which corresponds to a quadratic factor of the polynomial Pn(x). Bairstow's method extracts quadratic factors from a polynomial using only real arithmetic. The quadratic formula can then be used to determine the corresponding pair of real roots or complex conjugate roots.
