A Diagrammatic Approach For Polynomial Orders
Sergey P. Tromov
Electronic Devices, Vol. 13, No. 2, 2024.
DOI: https://doi.org/10.6025/ed/2024/13/2/57-66
Link: https://www.dline.info/ed/fulltext/v13n2/edv13n2_3.pdf
Abstract:
A diagram of a polynomial of the nth degree in the real number line helps us identify all the real solutions. The number of real solutions can range from 0 to n. The remaining solutions are complex and not directly shown by the diagram. In the article, besides the diagram of the fundamental polynomial, two additional diagrams are created, which enable us to depict all complex solutions on the same real number line. The use of this approach is thoroughly explored for solving a cubic polynomial. In this scenario, the approach exhibits unique characteristics compared to polynomials of different degrees. Considering well-known formulas for the solutions of polynomials of degrees 3 and 4, the additional diagrams of the approach provide precise formulas for polynomials of order n up to 10.