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Chapter 3: Problem 81

What is a polynomial inequality?

Short Answer

Expert verified
A polynomial inequality is a type of inequality that involves a polynomial. It is solved by finding the roots of the polynomial, dividing the number line into intervals, and substituting values from each interval into the equation to determine the solution set.

Step by step solution

01

Definition

A Polynomial Inequality is an inequality that involves a polynomial. Basically, it's an inequality which includes a polynomial expression. Instead of being equal to each other, the expressions are either greater than, less than, or not equal to each other.
02

Explanation of the Parts

The simplest type of polynomial inequality has the form \(P(x) > 0\), \(P(x) < 0\), \(P(x) 鈮� 0\), or \(P(x) 鈮� 0\), where \(P(x)\) is a polynomial function.
03

Solving

To find the solution of the inequality, we find the roots of the polynomial and use these to define intervals on the number line. Substituting a value from each interval into the polynomial provides the sign of the polynomial in that interval, which allows us to solve the inequality.

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Most popular questions from this chapter

The equation for \(f\) is given by the simplified expression that results after performing the indicated operation. Write the equation for \(f\) and then graph the function. $$ \frac{x}{2 x+6}-\frac{9}{x^{2}-9} $$

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