In these worksheets, students will determine whether the roots of quadratic equations in standard form are real, complex, rational, and/or equal.

#### What is The Discriminant? There are so many questions in math that are confusing. Topics, operations, definitions... and the list just goes on and on. But here’s the thing, if you pay a little bit of concentration, and spend some time practicing the questions over and over, it isn’t actually that tough. And sometimes, math is really fun and quite interesting too! Imagine all the new things you get to learn! So do you know what "discriminant" means in math? Let's take a look at it together! The term underneath the square root in the quadratic formula is known as discriminant. It tells us the number of solutions to a quadratic equation. If the discriminant is positive, it means that we have 2 solutions. If the discriminant is negative, it means that there are no solutions. And if the discriminant is equal to zero, it means we have one solution. To calculate the discriminant, we square the "b" term and subtract it 4 times the "a" term times the "c" term.

Your students will use these worksheets to learn how to find the discriminant of a quadratic equation. The discriminant indicates what type of root the equation has and helps to solve the quadratic equation. Students will learn how to determine whether the roots are real, complex, rational, and/or equal. when given values for the discriminants. They will then work with quadratic equations in standard form to answer questions about the roots of quadratic equations. They will also determine whether or not a given set of numbers can be the roots to a quadratic equation. This set of worksheets contains step-by-step solutions to sample problems, both simple and more complex problems, a review, and a quiz. When finished with this set of worksheets, students will have demonstrated skill in working with the nature of roots of quadratic equations. These worksheets explain how calculate the determinant of a 2x2 matrix using simple cross multiplication and subtraction. Sample problems are solved and practice problems are provided.

# The Discriminant Worksheets

## The Discriminant Lesson

Students will find the nature of the roots of the equation. In a quadratic equation (ax2 + bx + c = 0), discriminant is given as b2 - 4ac

## Discriminant Worksheet

Students will examine whether the following series of equations have real roots. Ten problems are provided.

## The Discriminant Practice

Students will practice making determinations about the roots of quadratic equations. Ten problems are provided.

## The Discriminant Review

The concept of the nature of roots (real, complex, rational, equal, etc.) of quadratic equations is reviewed. A sample problem is solved and six practice problems are provided.

## The Discriminant Quiz

Students will demonstrate their proficiency with understanding the full idea of the discriminant. Ten problems are provided.

## The Discriminant Check

Students will answer questions about all aspects of a series of quadratic equations. Three problems are provided, and space is included for students to copy the correct answer when given.