1. What is the Rational Zeros Theorem?

The Rational Zeros Theorem provides a complete list of possible rational zeros (or roots) of a polynomial function with integer coefficients. It states that any possible rational zero of a polynomial is of the form ±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 Zeros 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 the constant term and leading coefficient, then computes all possible ±p/q combinations.

3. Importance of Rational Zeros

Details: Finding rational zeros is the first step in factoring polynomials and solving polynomial equations. It helps narrow down potential solutions before applying other methods.

4. Using the Calculator

Tips: Enter the constant term and leading coefficient as integers. The calculator will list all possible rational zeros (positive and negative fractions in reduced form).

5. Frequently Asked Questions (FAQ)

Q1: Does this guarantee actual zeros of the polynomial?
A: No, it only lists possible candidates. You still need to test which ones are actual zeros.

Q2: What if my polynomial has non-integer coefficients?
A: The theorem only applies to polynomials with integer coefficients. Multiply through by denominators to convert to integer coefficients first.

Q3: How do I know which possible zeros to test first?
A: Typically start with the simplest fractions (±1, ±2, etc.) before testing more complex fractions.

Q4: What if there are no rational zeros?
A: The polynomial may have irrational or complex zeros. The theorem only identifies possible rational ones.

Q5: Can this be used for polynomials of any degree?
A: Yes, the theorem applies to polynomials of degree 1 or higher with integer coefficients.