1. What is the Rational Zero Theorem?

The Rational Zero Theorem helps identify all possible rational zeros (roots) of a polynomial function with integer coefficients. It states that any possible rational zero of a polynomial is a fraction p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

2. How Does the Calculator Work?

The calculator uses the Rational Zero Theorem:

Where:

• Constant Term — The term without any variables (a₀)
• Leading Coefficient — The coefficient of the highest degree term (aₙ)

Explanation: The calculator finds all factors of both numbers, then generates all possible ± combinations of their ratios.

3. Importance of Finding Rational Zeros

Details: Identifying possible rational zeros is the first step in solving polynomial equations. It helps narrow down potential solutions before applying synthetic division or other methods.

4. Using the Calculator

Tips: Enter the constant term and leading coefficient as integers. The leading coefficient cannot be zero. The calculator will list all possible rational zeros.

5. Frequently Asked Questions (FAQ)

Q1: Does this guarantee the polynomial has rational zeros?
A: No, it only lists possible candidates. The polynomial might have irrational or complex zeros instead.

Q2: What if my polynomial has non-integer coefficients?
A: The theorem only applies to polynomials with integer coefficients. You may need to multiply through to eliminate fractions.

Q3: How do I test which zeros are actual roots?
A: Use synthetic division or substitution to test each possible zero in the polynomial equation.

Q4: What if there are repeated factors?
A: The calculator shows each unique ratio only once, even if it comes from multiple factor combinations.

Q5: Can this find all roots of a polynomial?
A: Only potential rational roots. Higher degree polynomials may require additional methods to find all roots.