1. What is the Rational Root Theorem?

The Rational Root Theorem states that any possible rational zero of a polynomial with integer coefficients 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 Root Theorem formula:

Where:

• Constant Term — The term in the polynomial without a variable
• Leading Coefficient — The coefficient of the highest degree term

Explanation: The calculator finds all factors of the constant term and leading coefficient, then computes all possible ±p/q combinations.

3. Importance of Rational Root Theorem

Details: The theorem helps in solving polynomial equations by narrowing down possible rational solutions, saving time in trial-and-error methods.

4. Using the Calculator

Tips: Enter the constant term and leading coefficient as integers. The calculator will display all possible rational zeros based on the theorem.

5. Frequently Asked Questions (FAQ)

Q1: Does the theorem guarantee that listed zeros are actual roots?
A: No, it only lists possible candidates. You still need to test which ones are actual roots.

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 of the possible zeros are actual roots?
A: Use synthetic division or substitution to test each possible zero in the polynomial.

Q4: What about irrational or complex roots?
A: The Rational Root Theorem only identifies possible rational roots. Other methods are needed for irrational or complex roots.

Q5: Can the leading coefficient be negative?
A: Yes, the calculator works with both positive and negative integers for both coefficients.