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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

Input Fields
If enabled, the result will update automatically when you change any value.

Quartic Equation Formula

Formula
$$ax^4 + bx^3 + cx^2 + dx + e = 0$$

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.

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