Quartic Equation Solver
Roots of a degree-four polynomial
About this calculator
The Quartic Equation Solver finds all four roots of ax⁴ + bx³ + cx² + dx + e = 0 over the complex numbers using Ferrari's method: the equation is depressed by x = y − b/(4a), biquadratics factor through u = y², and the general case splits into two quadratics via the resolvent cubic. Arithmetic runs at 30-digit decimal precision, complex roots come as conjugate pairs, and the exact 16-term quartic discriminant flags repeated roots. Root counts are classified automatically.
How to use the Quartic Equation Solver calculator
- Enter the values for your problem into the input fields.
- Read the result — it updates instantly as you type.
- Check the formula and the visual explanation to follow how the answer was found.
- Copy the page URL to share the exact calculation.
Common examples
- x⁴ − 5x² + 4 = 0 → four real roots −2, −1, 1, 2
- x⁴ − 16 = 0 → x = ±2 and the imaginary pair ±2i
- x⁴ + 1 = 0 → four complex roots ±0.7071… ± 0.7071…i on the unit circle
- x⁴ − 4x³ + 6x² − 4x + 1 = 0 → quadruple root x = 1, flagged as repeated (Δ = 0)
Frequently asked questions
How does the Quartic Equation Solver calculator work?
Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.
When would I use the Quartic Equation Solver calculator?
It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.
How accurate are the results?
Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.