Rational Zeros Theorem Calculator
Find possible rational zeros using Rational Root Theorem. Candidates = ±(factors of constant) / (factors of leading coefficient).
Formula
Possible Rational Zeros = ±(factors of constant term) / (factors of leading coefficient)
- Rational Root Theorem helps find rational zeros of polynomials
- Not all candidates are actual zeros - must test each
- Test by substituting into polynomial or using synthetic division
- Works only for integer coefficients
Example
Inputs
- Constant Term: 12
- Leading Coefficient: 2
For x³+2x-12: constant=12 (factors: 1,2,3,4,6,12), leading=2 (factors: 1,2). Candidates: ±1, ±2, ±3, ±4, ±6, ±12, ±1/2, ±3/2, ...
Frequently asked questions
What's Rational Root Theorem?
If p/q is a rational zero in lowest terms, p divides the constant term and q divides the leading coefficient.
Are all candidates actual zeros?
No. These are just candidates. You must test each one in the polynomial.