Development of Calculator for Finding Complex Roots of n-th Degree Polynomials

Abstract

Software as a learning medium has become a trend in society. The development of science and technology encourage modernization in every field of education, including mathematics. One of the mathematical models often used is polynomial equation. Many mathematicians have done research on solving polynomials by using numerical algorithms, but only focus on mathematical analysis. In this research, design and construction of a calculator as a medium of learning has been done. The calculator is completed by many algorithm such as the quadratic formula, Cardano, Viete's, Bairstow, revise Baristow, Muller, and combination algorithms. The alculator was designed by UML approach and implemented on Java Swing GUI. The test results using black box method showed that 100%  of functional calculator can work well. Based on the average calculation error, cubic polynomial is solved properly by using Cardano algorithm which the average error is 1.43568059121049E-13%. Revise Bairstow algorithm showed good performance to find the complex roots of 4^th degree polynomial with an average error is 1.34421873307271E-09% and average of iteration is 4. The best combination algorithm on solving n^th degree polynomials is Muller-Cardano which has an average error 4.27781615793958E-13% and Revise Bairstow-Cardano with average number of iteration is 7 iterations.