J. Comp. Math., 3 (1985), pp. 161-166. The Computational Complexity Of The Resulatant Method For Solving Polynomial Equations Xiao-Hua Xuan 11 Hangzhou University, China Received 1984-7-21 Revised Online 2006-11-19 Abstract Under an assumption of distribution on zeros of the polynomials, we have given the setimate of computational cost for the resultant method. The result in that, in probability $1-\mu$, the computational cost of the resultant method for finding $\epsilong-approximations$ of all zeros is at most $cd^2(log d+log\frac{1}{\mu}+loglog\frac{1}{\epsilong}$, where the cost is measured by the number of f-evaluations. The estimate of cost can be decreased to $c(d^2log d+ d^2log\frac{1}{\mu}+d loglog\frac{1}{\epsilong})$ by combining resultant method with parallel quasi-Newton method. Key words: