1. What is the Rational Zero Theorem?

The Rational Zero Theorem states that any possible rational zero of a polynomial function is given by ±(factor of the constant term)/(factor of the leading coefficient). It helps identify potential roots of polynomial equations.

2. How Does the Calculator Work?

The calculator uses the Rational Zero Theorem formula:

Where:

• \( \text{factors\_p} \) — Factors of the constant term (p)
• \( \text{factors\_q} \) — Factors of the leading coefficient (q)

Explanation: The calculator generates all possible combinations of p/q and -p/q from the provided factors.

3. Importance of Rational Zero Theorem

Details: This theorem is crucial for solving polynomial equations as it narrows down the possible rational roots that need to be tested.

4. Using the Calculator

Tips: Enter comma-separated factors of the constant term (p) and leading coefficient (q). For example, if p=6 and q=2, enter "1,2,3,6" for p and "1,2" for q.

5. Frequently Asked Questions (FAQ)

Q1: Does this find all roots of a polynomial?
A: No, it only identifies possible rational roots. A polynomial may have irrational or complex roots as well.

Q2: What if none of the possible zeros work?
A: The polynomial may have irrational roots or your input factors may be incomplete.

Q3: How do I find the actual factors of a number?
A: List all integers that divide the number evenly without remainder.

Q4: Can this handle fractions as input?
A: No, enter only integer factors. The calculator will generate the fractional possibilities.

Q5: What's the difference between zeros and roots?
A: They are essentially the same - values that make the polynomial equal to zero.