Polynomial root calculator for iPhone
Enter any polynomial from degree 1 to 20 and get every root — real and complex — instantly, right here in your browser.
Roots and graph appear here once you solve.
What it solves
| Equation type | Example |
|---|---|
| Linear (degree 1) | 3x + 6 = 0 |
| Quadratic (degree 2) | x² − 5x + 6 = 0 |
| Cubic (degree 3) | x³ − 6x² + 11x − 6 = 0 |
| Quartic (degree 4) | x⁴ − 5x² + 4 = 0 |
| Higher degree | up to degree 20 |
Why most calculators stop at quadratics
The quadratic formula gives you an exact answer for degree 2. Degree 3 and 4 have formulas too, but they are long enough that most apps skip them. Above degree 4 there is no general formula at all — the Abel–Ruffini theorem proves one cannot exist — so roots have to be found numerically.
Solve f(x) uses exact symbolic solutions where they exist and numerical methods above that, so you get every root either way, including complex roots that come in conjugate pairs.
How to use it
Enter coefficients directly
Pick the degree, type the coefficients highest power first, and click Solve (or just press Enter). For x² − 5x + 6 you enter 1, −5, 6.
Or type the equation naturally
Switch to freeform entry and write it the way it appears in your textbook, like 3x^4 - 2x^2 + 7x - 1.
Read the graph
The graph plots the polynomial across a range scaled to fit the real roots, with each real root marked directly on the x-axis.
Frequently asked questions
Is this calculator free?
Yes, entirely. Every degree, real and complex roots — no account, no limits, no catch.
What is the highest degree it can solve?
Degree 20. Degrees 1 and 2 use exact formulas; degree 3 and above use Durand-Kerner numerical iteration to find every root simultaneously.
Can it find complex roots?
Yes. Complex roots are shown in a + bi form and always appear in conjugate pairs for polynomials with real coefficients.
What is the difference between a root and a zero?
They are the same thing. A root of the polynomial p(x) is any value of x where p(x) equals zero.
Why is there no formula for degree 5 and above?
The Abel–Ruffini theorem proves that no general formula using radicals can exist for degree 5 or higher — not that nobody has found one yet, but that one provably cannot exist. Numerical methods like Durand-Kerner are used instead.
Does it show step-by-step working?
No. It gives you every root and a graph, not a worked derivation — being upfront about that rather than implying otherwise.
Prefer it on your phone?
This calculator needs nothing beyond your browser, but the iPhone app goes further: it works with zero internet connection at all — useful in an exam room or mid-flight — keeps a history of everything you've solved, and its inputs are built for a phone keyboard instead of a desktop one.
Get Solve f(x) for iPhoneGet in touch
Found a bug or have a feature request? Email mosse692@gmail.com.
Download on the App Store