Equation Solver

Solve polynomial equations up to cubic degree and visualize their roots.

Parameters

ax + b = 0

x + = 0

ax² + bx + c = 0

x² + x

+ = 0

ax³ + bx² + cx + d = 0

x³ + x²

+ x +

= 0

Roots

Equation Solver & Numerical Roots Handbook

Mathematical Principles & Theorems

Solves polynomial and transcendental equations \(f(x) = 0\). Linear equations \(ax + b = 0 \implies x = -b/a\); Quadratic formula \(x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\) with discriminant \(\Delta = b^2-4ac\) governing real/complex roots; Cubic equations via Cardano-Tartaglia method; General root-finding via Newton-Raphson iteration \(x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}\) achieving quadratic convergence for regular roots.

Operating Instructions

Select solver type: Linear, Quadratic, Cubic, or Newton-Raphson General Solver.
Enter polynomial coefficients \(a, b, c, d\) or target equation string.
Click Solve to compute exact analytic radicals or numerical approximations.
Inspect the interactive 2D function graph to visualize root intercepts and tangent iterations.