1. What is the Rational Root Theorem?

The Rational Root Theorem states that any possible rational zero of a polynomial equation with integer coefficients must be 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 without any variables (a₀)
• Leading Coefficient — The coefficient of the highest degree term (aₙ)

Explanation: The theorem provides all possible rational roots, but not all may be actual roots of the polynomial.

3. Importance of Rational Root Test

Details: This test is crucial for solving polynomial equations as it narrows down the possible rational solutions, saving time in finding actual roots.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Does this find all roots of a polynomial?
A: No, it only lists possible rational roots. There may be irrational or complex roots not identified by this theorem.

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 by the LCD to convert to integer coefficients.

Q3: How do I know which of these are actual roots?
A: You need to test each possible root by substituting into the polynomial or using synthetic division.

Q4: What if the leading coefficient is 1?
A: Then the possible rational zeros are simply the factors of the constant term (positive and negative).

Q5: Can this theorem guarantee a rational root exists?
A: No, it only says that if there are rational roots, they must be among the listed possibilities.