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 ax2+bx+c=0, a quadratic inequality can be written in the form ax2+bx+c  0, where is <, >, , or . Here are some examples of quadratic inequalities:

x24x5<0 and 12 x2+4x70.

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: x24x5>0.

Solution

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