Rational Zero Theorem Calculator
Introduction & Importance
The rational zero theorem is a crucial tool in polynomial division and factoring. Our calculator helps you find rational roots quickly and accurately.
How to Use This Calculator
- Enter the coefficients of the polynomial in the ‘n’ and ‘d’ fields.
- Click ‘Calculate’.
- View the results below the calculator.
Formula & Methodology
The rational zero theorem states that if a polynomial p(x) has a rational root r/s, then r divides p(x) and s divides p(x).
Real-World Examples
Example 1
Find the rational roots of p(x) = 3x^3 – 5x^2 + 2x – 6.
| n | d | p(n/d) |
|---|---|---|
| 3 | 1 | 3 |
| 3 | 2 | -1 |
| 6 | 1 | -6 |
The rational roots are -2 and 3.
Example 2
Data & Statistics
| Polynomial | Rational Roots |
|---|---|
| 3x^3 – 5x^2 + 2x – 6 | -2, 3 |
| x^4 – 3x^3 + 2x^2 – x + 5 | 1, 5 |
Expert Tips
- Always check for obvious rational roots first.
- Use synthetic division to confirm rational roots.
- For higher degree polynomials, consider using other factoring techniques.
Interactive FAQ
What is a rational root?
A rational root is a root that can be expressed as a fraction p/q, where p and q are integers and q is not zero.