# Ch 19: Real, Complex & Rational Zeros

### About This Chapter

## Real, Complex & Rational Zeros - Chapter Summary and Learning Objectives

Use the lessons in this chapter to boost your knowledge of real, complex and rational zeros. Expert instructors have compiled materials and created lessons you can explore to get full comprehension of this subject area. The lessons take a close look at real zeros of polynomials, offering examples to help enhance your understanding. This chapter also explores the mathematical operations involved in finding complex and rational zeros in algebra, and helps you get a great grasp of how to use rational and complex zeros to write polynomial equations.

Some lessons are available as videos, with full transcripts displaying easy-to-identify vocabulary words. Text lessons also feature highlighted key words. Review the lessons in any sequence you desire, and revisit them as many times as you'd like until you've gotten the gist of the materials. Take the self-assessment quiz with each lesson, along with a more comprehensive chapter exam to gauge your knowledge of real, complex and rational zeros. Reviewing the lessons will help you learn:

- The basics of real zeros of polynomials
- How to find complex zeros of a polynomial function
- Ways to find rational zeros using the rational zeros theorem and synthetic division
- Steps for writing polynomial equations by using rational and complex zeros

Lesson | Objective |
---|---|

Real Zeros of Polynomials | Learn the meaning and a description of real zeros of polynomials. |

Finding Complex Zeros of a Polynomial Function | Understand how to find complex zeros of a polynomial function. |

Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division | Examine rational zeros theorem, and learn how to apply the theorem to find zeros of polynomial functions. |

Using Rational & Complex Zeros to Write Polynomial Equations | Study how to write a polynomial function from its given zeros, and learn how to follow steps that convert zeros into factors and then factors into polynomial functions. |

### 1. Real Zeros of Polynomials

In this lesson, we'll tackle polynomial equations and learn how to solve for their zero values. We'll also work through some sample problems using Descartes' Rule of Signs.

### 2. Finding Complex Zeros of a Polynomial Function

This lesson will explain how to find complex zeros of a polynomial. You will be shown examples to apply factoring and the quadratic formula or square roots to solve for complex zeros.

### 3. Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division

After completing this lesson, you will know what the rational zeros theorem says. You will also know how to apply this theorem to find zeros of polynomial functions.

### 4. Using Rational & Complex Zeros to Write Polynomial Equations

In this lesson, you will learn how to write a polynomial function from its given zeros. You will learn how to follow a process that converts zeros into factors and then factors into polynomial functions.

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### Other Chapters

Other chapters within the Intermediate Algebra for College Students course

- Algebra Review
- Number Theory Principles
- Exponents & Their Properties
- Radicals
- Polynomials
- Rational Expressions & Practice
- Linear Equations, Systems & Graphs
- Linear Inequalities
- Absolute Value Expressions & Graphs
- Complex Numbers, Forms & Graphs
- Quadratic Equations & Solutions
- Logarithmic & Trigonometric Equations
- Cartesian Coordinate System
- Linear Models
- Types of Functions
- Graphing & Transforming Functions
- Quadratic & Polynomial Functions
- Operations on Functions
- Rational Functions & Inequalities
- Pythagorean Theorem
- Probability Calculations
- Measurement & Unit Conversion