Polynomial Equation Solver

A polynomial equation solver that finds all real and complex roots of polynomial equations of any degree.

What is a Polynomial Equation?

A polynomial equation is an equation of the form:

a_nxⁿ + a_n-1x^n-1 + ... + a₁x + a₀ = 0

where n is a non-negative integer (the degree), and a₀, a₁, ..., aₙ are coefficients with aₙ ≠ 0.

How Does the Polynomial Solver Work?

This calculator uses numerical methods to find polynomial roots:

• For degree 1: Direct solution using linear equation formula
• For degree 2: Quadratic formula for exact solutions
• For degree 3: Cubic formula or numerical approximation
• For degree 4+: Numerical root-finding algorithms (Newton-Raphson method)

Applications of Polynomial Equations

Polynomial equations are fundamental in mathematics and appear in various fields:

• Physics: Motion equations, wave functions, and quantum mechanics
• Engineering: Signal processing, control systems, and structural analysis
• Economics: Cost functions, revenue optimization, and market modeling
• Computer Graphics: Curve fitting and interpolation
• Chemistry: Equilibrium calculations and reaction kinetics