Polynomial Equation Solver

A polynomial equation is an algebraic expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Finding the roots (or zeros) of these equations is a foundational task in mathematics. Our Polynomial Solver is a high-precision maths solver built to handle equations of any degree.

From the simple quadratic equations taught in early algebra to the complex quintic and higher-degree polynomials used in modern engineering, this tool provides instant solutions and graphical visualizations. As defined by Britannica, the highest power of the variable determines the "degree" of the polynomial.

The Fundamental Theorem of Algebra

A key principle in our solver's logic is the Fundamental Theorem of Algebra, which states that every non-zero, single-variable polynomial of degree n has exactly n complex roots. Our tool identifies both real and imaginary components, ensuring a complete mathematical picture.

Solving by Degree

Practical Use Cases

Polynomials are widely used in a variety of scientific fields. For instance, in Physics, the trajectory of a projectile under gravity is a quadratic polynomial. In Economics, cost and revenue functions are modeled as high-degree polynomials to account for fluctuating scales. Research from NIST frequently applies polynomial modeling in materials science.