Polynomial Solver
Find the roots of polynomials up to degree 4.
Roots
—
Enter coefficients
x₁
—
x₂
—
x₃
—
x₄
—
Factored Form
—
Discriminant
—
Polynomial Roots
A root of a polynomial is a value x where f(x) = 0. The Fundamental Theorem of Algebra states that a polynomial of degree n has exactly n roots (counting multiplicity).
Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a
Discriminant
For ax² + bx + c = 0: Δ = b² - 4ac
- Δ > 0: Two distinct real roots
- Δ = 0: One repeated real root
- Δ < 0: Two complex conjugate roots
Cubic and Quartic
Cubic equations have exact solutions (Cardano's formula). Quartic equations can be solved using Ferrari's method. Higher-degree polynomials typically require numerical methods.