1 A Blended Root-Finding Algorithm to Solve Nonlinear Equations Srinivasarao Thota * , V. Lakshmi Chetana † , Thulasi Bikku † ∗ Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Amaravati, Andhra Pradesh–522503, India † Department of Computer Science Engineering, Amrita School of Computing, Amrita Vishwa Vidyapeetham, Amaravati, Andhra Pradesh–522503, India Email: srinithota@ymail.com, s_lakshmichetana@av.amrita.edu, b_thulasi@av.amrita.edu Abstract This paper focus on a new blended root-finding algorithm to solve the given transcendental/ nonlinear equations. This algorithm is based on the classical methods, namely Newton- Raphson method and trisection method. One of the advantages of the proposed algorithm is not only fast converging but also guarantee the root. The proposed algorithm is easy to understand and one can implement this algorithm in any mathematical software tools. Several numerical examples are presented to illustrate the algorithm and comparisons are made to show the efficiency of the proposed algorithm. Keywords: Root-finding algorithms, Newton-Raphson method, Trisection method, Hybrid algorithms, Transcendental equations. * Corresponding Author. Email: t_srinivasarao@av.amrita.edu International Conference on Connecting Theory and Practice in Mathematics, Statistics, and Data Science (ICMSD-2025) jointly organized by Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology-AP University (VIT-AP), India, and Department of Mathematics and Statistics, The University of the West Indies, Trinidad and Tobago. March 15–17, 2025