Lesson 4

Open your copy of the Lesson 4 Assignment, which you saved in your course folder at the start of this lesson. Complete the assignment.

Go to Module 4 Project: Imagineering. Complete Step 2: Feasibility Study.

Save all your work in your course folder.

Going Beyond

Have you ever seen the humorous cartoon shown on the T-shirt in the illustration? Think you’ve got it easy when the discriminant shows that there are no real roots? After all, if there are no real roots, then there are no solutions, right? Not so fast. Mathematicians have a way of talking about such roots by introducing the concept of imaginary units. The imaginary unit, i, is defined as the square root of −1. In other words,

The following shows some examples of how you can simplify expressions involving the imaginary unit.

Solve the following quadratic equations that have no real roots.

1. x2 + 4x + 10 = 0
   
   
2. 5x2 − 2x + 1 = 0

If you pursue a career in engineering or mathematics or a science-related field, you may encounter imaginary units and complex numbers in your studies. You may want to search the Internet for information about these types of numbers and how they are applied in these different fields.