Polynomial Solver
Find rational roots of a polynomial up to degree 6 using the rational root theorem.
Inputs
Comma-separated, e.g. '1,-6,11,-6' for x³−6x²+11x−6
Rational Roots Found
1, 2, 3
Degree
3
Candidates Tested
8
Step by step
Values used
Coefficients (highest to lowest degree) = 1,-6,11,-6
Rational Root Theorem
Candidates: ±(factors of constant term) / (factors of leading coefficient)
Rational Roots Found
= 1, 2, 3
Degree
= 3
Candidates Tested
= 8
How it works
The Rational Root Theorem states that any rational root p/q of a polynomial with integer coefficients must have p dividing the constant term and q dividing the leading coefficient. This calculator tests all such candidates and deflates the polynomial via synthetic division when a root is found.
Formula
Rational Root Theorem
Candidates: ±(factors of constant term) / (factors of leading coefficient)
- p
- Factor of constant term
- q
- Factor of leading coefficient
Frequently Asked Questions
What if the polynomial has irrational roots?
This calculator only finds rational roots. Irrational or complex roots will not be detected — use the cubic or quartic solver for those.
What format should the coefficients be in?
Enter comma-separated numbers from the highest degree to the lowest. For x³−6x²+11x−6, enter 1,-6,11,-6.