Fourth-Degree Equation Calculator
Find the roots of quartic equations
Fourth-Degree Equation Calculator
Provide the coefficients of ax^4 + bx^3 + cx^2 + dx + e = 0. The solver applies Durand–Kerner iterations and reports both real and complex roots.
Table of Contents
How to Use
- Enter coefficients for a, b, c, d, and e.
- Ensure the leading coefficient a is non-zero.
- Run the calculator to view real and complex roots along with the normalized polynomial.
How the solver works
Durand–Kerner (Weierstrass) iterations update all roots simultaneously. Initial guesses are spread on a circle and refined until they satisfy the polynomial within a small tolerance.
Tips for stable input
- Scale coefficients so that a is near 1 for faster convergence.
- Large coefficients can lead to floating-point noise; normalize when possible.
- Repeated roots may appear multiple times in the real or complex lists.
Frequently Asked Questions
- Does the calculator handle complex roots?
- Yes. Complex conjugate pairs are listed with their real and imaginary parts rounded to six decimals.
- Can I trust the number of iterations?
- The iteration count reflects how many refinement passes were required before the tolerance threshold was reached. Most well-scaled problems converge in fewer than 20 steps.