Back To Course

SAT Mathematics Level 2: Help and Review22 chapters | 225 lessons

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

The discriminant helps you to solve quadratic equations. In this lesson, you will learn how to identify the discriminant and how to use it to help you find the number of solutions in a quadratic equation.

The discriminant is easy to find when you look at the **quadratic formula**. The quadratic formula is the equation you use to find the solutions to quadratic equations. It looks like this:

The **discriminant** is the part inside the square root. Take a moment to look for the square root and find what is inside the square root. Once you see it, you will have found the discriminant. If we isolate that part, we get the formula for finding the discriminant, which is this:

The discriminant tells you how many possible solutions a particular quadratic equation has. Before we can use the quadratic equation, though, we first have to change it to **standard form**. Standard form is when all the variables and constants are on one side of the equation, and the other side is a zero. It looks like this:

Once you have your quadratic equation in standard form, you can label your numbers with the appropriate letters and plug the values into your formula for finding the discriminant. The result of your discriminant tells you how many solutions your quadratic has.

Let's look at an example:

In our example, our quadratic equation gives us 1 for our letter *a*, 5 for letter *b*, and 4 for letter *c*. We take these values and plug them into their appropriate places in the discriminant formula, and we'll find that our discriminant equals 9, a positive number. This tells us that our quadratic equation has two possible real solutions. Real solutions are solutions that can be calculated using the quadratic formula. When you graph this quadratic equation, you will see that the curve crosses the *x*-axis in two places, exactly where your solutions are.

While the discriminant tells us the number of possible solutions, it does not tell us what those solutions are. But, it does give us a clue as to how many solutions we need to look for.

Remember that, when there are no numbers in front of variables, it is assumed that there is a 1 in front. We don't write the 1 because it is a mathematical convention and because it looks neater, especially when you have a lot of letters to work with.

Let's look at another example:

We have labeled our letters with their appropriate values. After plugging the appropriate values into our discriminant formula, we find that our discriminant is -31, a negative number. Hmmâ€¦ what could this mean? When the discriminant is negative, it means that there are no real solutions. What this means is that, when you graph the equation, you will see that it never crosses the *x*-axis and therefore has no real solutions.

There is one other possible situation - when the discriminant equals 0. When you see this, it means that there is only one possible real solution. When graphed, the equation will touch the *x*-axis only at one point.

Here is a chart to help you remember the possible discriminant situations and what they mean:

Discriminant | # of Solutions |
---|---|

> 0 | Two real solutions |

= 0 | One real solution |

< 0 | No real solutions |

To summarize, the discriminant helps you by telling you how many possible solutions a quadratic equation has. The formula can be found by looking for the square root symbol in the quadratic formula. There are three possible scenarios. If the discriminant is a positive number, then there are two real solutions. If the discriminant equals 0, then there is only one real solution. If the discriminant is a negative number, then there are no real solutions.

Following this lesson, you'll have the ability to:

- Define the discriminant and recall its purpose
- Explain how to find the discriminant
- Describe the possible scenarios when using the discriminant

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Log in here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
5 in chapter 2 of the course:

Back To Course

SAT Mathematics Level 2: Help and Review22 chapters | 225 lessons

- Evaluating Square Roots of Perfect Squares 5:12
- Estimating Square Roots 5:10
- Simplifying Square Roots When not a Perfect Square 4:45
- Simplifying Expressions Containing Square Roots 7:03
- Discriminant: Definition & Explanation
- Square Root: Sign, Rules & Problems 10:15
- The Square Root Property 6:49
- Adding Square Roots
- Subtracting Square Roots
- Go to Square Roots: Help and Review

- SIE Exam Study Guide
- Indiana Real Estate Broker Exam Study Guide
- Grammar & Sentence Structure Lesson Plans
- Foundations of Science Lesson Plans
- Career, Life, & Technical Skills Lesson Plans
- Business Costs, Taxes & Inventory Valuations
- Using Math for Financial Analysis
- Assessments in Health Education Programs
- Governmental Health Regulations
- Understanding Health Education Programs
- AFOQT Prep Product Comparison
- ACT Prep Product Comparison
- CGAP Prep Product Comparison
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison

- What is Deadlock? - Definition, Examples & Avoidance
- El Hombre que se Convirtio en Perro: Author, Summary & Theme
- Achilles in The Iliad: Character Analysis & Description
- A Wrinkle in Time Chapter 5 Summary
- Roald Dahl Project Ideas
- Media Literacy Activities for High School
- Letter M Activities
- Quiz & Worksheet - Shang Dynasty Religion & Culture
- Quiz & Worksheet - Alternative Assessment Types
- Quiz & Worksheet - Population Composition
- Quiz & Worksheet - Minimalist Painters
- Analytical & Non-Euclidean Geometry Flashcards
- Flashcards - Measurement & Experimental Design
- Grammar Worksheets & Practice
- Responsible Decision-Making Teaching Resources

- OSAT Earth Science (CEOE) (008): Practice & Study Guide
- Honors Algebra 1 Textbook
- A Separate Peace Study Guide
- AEPA Geography (AZ004): Practice & Study Guide
- PLACE Reading Teacher: Practice & Study Guide
- The Ancient Hebrews: Homeschool Curriculum
- Thermal Energy: Help and Review
- Quiz & Worksheet - Cell Membrane Location & Characteristics
- Quiz & Worksheet - The Bodies of Sponges
- Quiz & Worksheet - Sponge Digestive System & Excretion
- Quiz & Worksheet - Cobb Douglas Production Function
- Quiz & Worksheet - Characteristics of Carnivores

- Dehydration Reaction: Definition & Examples
- Natural Selection Lesson for Kids
- Transition Words Lesson Plan
- Expository Writing Lesson Plan
- Debate Lesson Plan
- Homeschooling in Alabama
- How to Learn Spanish for Kids
- 8th Grade Science Projects
- How Long Does it Take to Learn Spanish?
- How to Pass Statistics
- California Alternative Teacher Certification
- Fun Math Games for 3rd Grade

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject