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Chapter 11: Problem 79

What is a polynomial inequality?

Short Answer

Expert verified
A polynomial inequality is a type of inequality where one polynomial expression is less than (<), less than or equal to (鈮�), greater than (>), or greater than or equal (鈮�) another.

Step by step solution

01

Definition

A polynomial inequality is a type of algebraic inequality where one polynomial expression is greater than or less than another. It's represented in the form \(P(x) > 0\), \(P(x) < 0\), \(P(x) \geq 0\), or \(P(x) \leq 0\), where \(P(x)\) is a polynomial function.
02

Explanation of terms

A polynomial is an expression made up of variables and coefficients, with only positive integer exponents. Inequality means there is a greater or less relation between the two sides of the equation.
03

Example

For example, in the polynomial inequality \(x^2 - 3x + 2 > 0\), the inequality is asking for which values of \(x\), if any, the quadratic polynomial \(x^2 - 3x + 2\) is greater than zero.

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Most popular questions from this chapter

Will help you prepare for the material covered in the first section of the next chapter. In exercise, use point plotting to graph the function. Begin by setting up a table of coordinates, selecting integers from \(-3\) to \(3,\) inclusive, for \(x\). \(f(x)=2^{x}\)

Simplify: \(\frac{1+\frac{2}{x}}{1-\frac{4}{x^{2}}}\).

Determine whether statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The inequality \(\frac{x-2}{x+3}<2\) can be solved by multiplying both sides by \(x+3,\) resulting in the equivalent inequality \(x-2<2(x+3)\).

Factor: \(1-8 x^{3} .\) (Section 6.4, Example 8)

Solve each equation by the method of your choice. $$\sqrt{2} x^{2}+3 x-2 \sqrt{2}=0$$
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