POLYNOMIAL ROOT finding process is an important topic in many applications, where it has been found that many functions and systems in practical life could be represented in polynomial form. Thus, this work develops a new approach for root finding technique for the complex coefficients polynomial form. This technique named semi-symbolic polynomial root finding, uses Newton-Raphson method with the idea of symbolic separation technique. In practical life, root-finding techniques face two major problems, accuracy and speed. Many methods were introduced, some of them concentrated on the accuracy and others concentrated on the speed. In this project, the Moore's program is taken as a technique that concentrates on the speed and the symbolic separated program is taken as a technique that concentrates on the accuracy. Also, from the results it was found that the semi-symbolic separated program is the best one among them since it really - gathers the points of accuracy and speed. The semi-symbolic separated program is also capable of solving polynomials of high degrees up to 270, which gives it the priority over the other two programs that have been mentioned above that could only reach degree 34. This priority answer the question why not using one of the available packages programs (like the Matlab package) that gives the solution for the polynomial with good percent of accuracy and speed? Where from the results it will be obvious that the Matlab package starts to give high error in the solution of a high degree polynomial.