Convolutional Neural Networks for Secure and Efficient Cubic Equation Solving

Conventional techniques such as Cardano's formula include complex calculations and are often performed. This study represents an effective and accessible approach to dealing with cubic equations by synthesis of numerical methods and algebraic procedures. We start with the conversion of the cubic equation into a depressive form, so it simplifies this problem while maintaining its basic properties. Subsequently, we use numerical techniques, such a Newton method or the Bisection method, to determine the roots of a depressive cubic equation. The roots are then used to restore the roots of the original cubic problem with algebraic transformations. In addition, we integrate the proposed access to the software application and offer an intuitive interface for solving cubic equations of various difficulties. The program provides features such as the graphical representation of the equation and its roots, as well as the choices for entering coefficients and the selection of preferred solutions. We show the efficiency and accuracy of our method in the effective solution of cubic equations through theoretical analysis and real practice.