Paper title: Numerical Methods for the Determination of Roots of Polynomials DOI: https://doi.org/10.4316/JACSM.201901005 Published in: Issue 1, (Vol. 13) / 2019Download Publishing date: 2019-04-16 Pages: 31-38 Author(s): AJAH Michael Abstract. The place of numerical approaches in determining the roots of polynomials cannot be overlooked. This is because the root of some polynomial equations cannot be determined by the analytic approaches and as such numerical methods have to be employed in doing so. In this research work, approximate roots of polynomials were found using numerical methods (the Bisection method, the Newton's method and the Secant method). The aim is to find out the more accurate method that converges quickly to the root of the polynomial and also stable when compared to the exact solution. The numerical methods were used to find solutions to problems of polynomials, results were analyzed and we found out that the Secant method is a more accurate and reliable numerical method in determining roots of polynomials as compared to the Bisection and Newton's methods. Keywords: Polynomial, Root/solution, Bisection Method, Newton's Method, Secant Method References: 1. K. Atkinson. A survey of numerical methods for the solution of Fredholm integral equations of the second kind. The Journal of Integral Equations and Applications, 15- 46, 1922. 2. J. Banas. Integrable solutions of Hammerstein and Urysohn integral equations. Journal of the Australian Mathematical Society, 46(1): 61-68, 1989. 3. A. Jerri. Introduction to integral equations with applications. John Wiley & Sons, second edition, 1999. 4. M. Bachar and M. Khamsi. On nonlinear Fredholm equations in Banach spaces. Journal of Numerical and Convex Analysis, 17(11): 2215-2223, 2016. 5. B. Mandal, and S. Bhattacharya. Numerical solution of some classes of integral equations using Bernstein polynomials. Applied Mathematics and computation, 190(2): 1707-1716, 2007. 6. E. Babolian, and A. Shahsavaran. Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets. Journal of Computational and Applied Mathematics, 225(1): 87-95, 2009. 7. A. Darijani, and M. Mohseni-Moghadam. Improved polynomial approximations for the solution of nonlinear integral equations. Scientia Iranica 20(3): 765-770, 2013. 8. K. Atkinson and H. Weimin. Numerical solution of Fredholm integral equations of the Second Kind. Theoretical Numerical Analysis. Springer, 473-549, 2009. 9. Y. Ikebe. The Galerkin method for the numerical solution of Fredholm integral equations of the Second Kind. SIAM Review, 14(3): 465-491, 1972. 10. B. Mandal and S. Bhattacharya. Numerical solution of some classes of integral equations using Bernstein polynomials. Applied Mathematics and computation, 190(2): 1707-1716, 2007. 11. Jumah Aswad Zarnan. A Novel Approach For The Solution Of A Class Of Urysohn Integral equations Using Bernstein Polynomials. Int. J. Adv. Res. 5(1), (2017) 2156-2162. 12. Jumah Aswad Zarnan. On The Numerical Solution of Urysohn Integral Equation Using Chebyshev Polynomial. International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:16 No:06 (2016), p.23-27 13. P. Davis, and P. Rabinowitz. Methods of numerical integration. Courier Corporation, 2007. Back to the journal content