We present a direction finding algorithm for diversely polarized arrays that is based on polynomial rooting. Using polynomial rooting instead of search reduces significantly the computational requirements of the algorithm and enhances resolution. The basic method is limited to linear uniformly spaced arrays. However, using an interpolation technique, the algorithm is extended to a larger class of arrays. The performance of the proposed algorithm is analyzed. Computer simulations are used to demonstrate the performance of the new technique and to verify the performance analysis.