## Finding and Using the Discriminant

#### Aligned To Common Core Standard:

**High School** - HSA-REI.B.4b

What Is a Discriminant? (In Math) Remember the quadratic formula?
For any quadratic equation like;
ax^{2} + bx + c =0
Here, we are discussing a part of the quadratic formula- the discriminant.
**THE DISCRIMINANT** -
The discriminant is that of a quadratic formula that is present under the square root, which is b^{2} - 4ac. The discriminant can be a positive number, a negative number, or a zero. It determines the number of possible solutions to the given quadratic equation
- A positive discriminant shows that a quadratic equation has two distinct real number solutions.
- A negative discriminant shows that neither of the two solutions is a real number.
- A zero discriminant shows that a quadratic equation has repeated a real number solution.
**EXAMPLE** - Suppose, you are asked to find out how many solutions the following quadratic equation has,
2x^{2} + 5x - 1 = 0
From the above equation, we get:
a= 2, b= 5, c= -1 putting these values in the discriminant, we get:
b^{2} – 4ac, (5)^{2} – 4(2)(-1), 25 - (-8), 25 + 8 = 33, 33 is a positive number, so it means that the quadratic has two solutions.

### Printable Worksheets And Lessons

- Finding the Discriminant
Step-by-step Lesson- This is an often overlooked, yet helpful
concept for all math students.

- Guided Lesson -
You want to know how overlooked this concept; MS Word marks the
word "Discriminant" as a misspelling in all contexts.

- Guided Lesson Explanation
- Breaking down parts of the Quadratic formula does make it seem
less obtrusive.

- Practice Worksheet -
It would be nice if they had more standards that broke down a formula
so deeply.

- Matching Worksheet
- Match the quadratic to the value of it's simplified discriminant.

#### Homework Sheets

This skill use to just apply to trigonometry, but we see it pop up with algebra more often now.

- Homework 1 - Find the value of the discriminant by breaking down what appears under the radical.
- Homework 2 - The discriminant of a quadratic equation (ax^2 + bx +c = 0) is b^2 - 4ac. It is the expression under the radial in the quadratic formula.
- Homework 3 - Four problems that are totally broken down for you.

#### Practice Worksheets

Kids often ask what the discriminant actually is. I usually just say it's your answer to a quadratic equation.

- Practice 1 - Apply the formula and run away with it. There is plenty of space to work with here.
- Practice 2 - How many moves can you do it in?
- Practice 3 - The discriminant can also tell you the nature of the possible solutions.

#### Math Skill Quizzes

See if you can spot the pattern I have going on in these.

### Why is This Value Important to Us?

The nature of this value is important for us to understand the different possible and types of solutions when working with quadratic equations. This is a great way to check your final answer. When working with these problems we can solve them in one of four different ways. Factoring can be used to condense and expand problem sets. We can use the complete the square method when we are dealing with complicated equations. We can also use the square root method to collect all the exponentials and place them to one side of the equation. If the quadratic is in standard form, we can simply use the quadratic formula to solve it. Which method we use to process these calculations is all dictated by understanding the spirit of the discriminant.