Solve Polynomial and transcendental Equations with use Generalized Theorem (Method Lagrange)

TL;DR

This paper introduces a Generalized Theorem that provides a new approach to solving polynomial and transcendental equations by analyzing the subfields of their roots, with applications in physics and astronomy.

Contribution

It presents a novel Generalized Theorem that links the roots of equations to subfields of functional terms, enabling solutions to complex equations like the Kepler equation.

Findings

Unified approach to roots based on subfields

Solutions to hyperbolic equations in sciences

Generalized solutions to Kepler and other equations

Abstract

The great innovation of the Generalized Theorem is that it gives us the philosophy to work out the knowledge that the number of roots of an equation depends on the subfields of the functional terms of the equation they generate. Thus, the final field of the roots of the equation will be the union of these subfields. We have a wide range of applications by solving hyperbolic in all sciences, especially in physics and chemistry. In this paper, we solve the generalized trinomial and some important applications in physics and astronomy like the generalized solution of the Kepler equation.