Quartic Equation Solver
This calculator helps you find the real and complex roots of a quartic (fourth-degree) polynomial equation of the form $$ax⁴ + bx³ + cx² + dx + e = 0$$. It’s useful for students, engineers, and anyone dealing with algebraic equations. Just enter the coefficients and get the exact roots instantly.
Quartic Equation Solver
Quartic Equation Formula
Solving a quartic equation analytically involves a complex process including substitution (Ferrari’s method), solving a resolvent cubic, and simplifying radicals. While it’s theoretically solvable, most practical calculators rely on numerical methods for quick results.
A quartic equation is a polynomial of degree 4. It may have up to 4 real or complex roots. The roots can be found using Ferrari’s method, which reduces the equation to a depressed quartic and solves a related cubic equation. While exact solutions are possible, in real-world applications, numerical approximations (like using the Newton-Raphson method) are often used for efficiency. This calculator automates that process and gives you immediate answers.