# 4.6 Polynomial Inequalities and Rational Inequalities

Solve polynomial inequalities.

Solve rational inequalities.

We will use a combination of algebraic methods and graphical methods to solve polynomial inequalities and rational inequalities.

# Polynomial Inequalities

Just as a quadratic equation can be written in the form $a{x}^{2}+bx+c=0$, a **quadratic inequality** can be written in the form $a{x}^{2}+bx+c\text{}\text{}0$, where is $<,\text{},\text{}\le $, or $\ne $. Here are some examples of quadratic inequalities:

When the inequality symbol in a polynomial inequality is replaced with an equals sign, a **related equation** is formed. Polynomial inequalities can be solved once the related equation has been solved.

# Example 1

Solve: ${x}^{2}-4x-5>0$.

# Solution

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