Rational Root Theorem Example
Let’s consider the example equation:
2x2 – 5x + 1
- Here, we need to find rational solutions, which are fractions in the form p/q. The leading coefficient is 2, and the constant term is 1.
- For this equation to have rational solutions, q must divide 2, and p must divide 1.
- As 1, has no divisors other than 1, and 2 can be divided by 1 or 2, the possible rational solutions are limited to 1/1 or 1/2 (0.5).
So, the equation can have solutions like x = 1 or x = 1/2
Note here that we aim to discover rational solutions in the form of a p/q
Rational Root Theorem
Rational Root Theorem also called Rational Zero Theorem in algebra is a systematic approach of identifying rational solutions to polynomial equations.
According to Rational Root Theorem, for a rational number to be a root of the polynomial, the denominator of the fraction must be a factor of the leading coefficient (the coefficient of the term with the highest power of the variable). Additionally, the numerator of the fraction must be a factor of the constant term (the term that doesn’t include the variable). This theorem is useful for narrowing down possible rational solutions to a polynomial equation.
Rational Root Theorem helps in the quick identification of rational solutions of polynomial equations. We can also find roots by using a specific formula or by factorizing the polynomial. In this article, we will discuss about rational root theorem in detail, with its examples, formula, and some solved examples to understand the concept of the Rational Root Theorem.
Table of Content
- What is the Rational Root Theorem?
- Rational Root Theorem Definition
- How to Find Rational Zeros?
- Rational Root Theorem Example
- Rational Root Theorem Proof
- How to Find Zeros using Rational Zero Theorem?
- Steps to Find Rational Zero
- Applications of Rational Root Theorem
- Solved Examples on Rational Root Theorem
- Rational Root Theorem Worksheet