SOLVING FOURTH-DEGREE ALGEBRAIC EQUATIONS: METHODS AND APPLICATIONS

This paper presents an in-depth exploration of solving fourth-degree algebraic equations (quartic equations) using various methods. The primary focus is on solving equations of the from demonstrating step-by-step approaches such as factorization the Ferrari method and the Newton-Raphson method. Examples are provided to show practical applications of these techniques including solving equations like .The paper also introduces software solutions to compute the roots of quartic equations using the,Math.Net Numerics library and algorithmic  approaches. Methods such as the Malles Oflvy and Leo Giugiuc techniques are examined showcasing how algebraic manipulation and numerical can be utilized to find the solutions to complex polynomial equations.

Keywords: Quartic equation, Factorization method, Ferrari’s method, Newton-Rapson method, Algebraic roots, Complex numbers, Polynomial equations, Numerical methods, Math.Net Numerics, Malles Oflvy method, Leo Giugiuc technique.