How do you calculate the discriminant for the equation $$3x^2 - 19x = -20$$ ?

First, rewrite the equation in standard form: $$3x^2 - 19x + 20 = 0$$ . Then, the discriminant is $$D = (-19)^2 - 4(3)(20) = 361 - 240 = 121$$ .

Solve the equation $$2x^2 + 2x - 12 = 0$$ using the quadratic formula.

Using the quadratic formula, we find $$x = \frac{{-2 \pm \sqrt{{2^2 - 4(2)(-12)}}}}{{2(2)}} = \frac{{-2 \pm \sqrt{{4 + 96}}}}{{4}} = \frac{{-2 \pm 10}}{{4}}$$ . Thus, $$x = 2$$ or $$x = -3$$ .

What is the first step in using the quadratic formula?

The first step is to identify the coefficients a, b, and c from the standard form of the quadratic equation $$ax^2 + bx + c = 0$$ .

What error did the student make when substituting values into the quadratic formula?

The student used $$b$$ instead of $$-b$$ as the first term in the numerator when substituting values into the formula.

If the discriminant is 76, what can we conclude about the solutions?

Since the discriminant is positive (76), we conclude that there are two distinct real solutions.

What is the correct setup of the discriminant for the equation $$3x^2 - 19x = -20$$ ?

The correct setup is $$(-19)^2 - 4(3)(20)$$ .

What is the value of the discriminant for the equation $$6x^2 - 2x - 3 = 0$$ ?

The discriminant is calculated as $$D = (-2)^2 - 4(6)(-3) = 4 + 72 = 76$$ .

How do you interpret a discriminant value of 29?

A discriminant value of 29 indicates that the quadratic equation has two distinct real solutions.

What is the general form of a quadratic equation?

The general form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where a, b, and c are constants and $$a \neq 0$$ .

Quadratic Formula and Discriminant Review Flashcards

Student preview

14 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the Quadratic Formula?

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What does the discriminant tell us about a quadratic equation?

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

What is the significance of a positive discriminant?

Back

A positive discriminant indicates that the quadratic equation has two distinct real solutions.

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

What is the significance of a zero discriminant?

Back

A zero discriminant indicates that the quadratic equation has exactly one real solution, also known as a repeated or double root.

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

What is the significance of a negative discriminant?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, but two complex solutions.

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

Create a free account and access millions of resources

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

7 questions

Places

Flashcard

•

KG - University

11 questions

Identify Parts of an Algebraic Expression and Evaluate

Flashcard

•

9th Grade

15 questions

5.4 Costs Flashcards

Flashcard

•

12th Grade

10 questions

2.4 - Information Management

Flashcard

•

11th Grade

9 questions

matematika kelas xi

Flashcard

•

11th Grade

10 questions

DNA Flashcards

Flashcard

•

9th - 12th Grade

15 questions

Flashcard - Unit Conversion and Practical Use

Flashcard

•

KG - University

Popular Resources on Wayground

5 questions

This is not a...winter edition (Drawing game)

Quiz

•

1st - 5th Grade

15 questions

4:3 Model Multiplication of Decimals by Whole Numbers

Quiz

•

5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

10 questions

The Best Christmas Pageant Ever Chapters 1 & 2

Quiz

•

4th Grade

12 questions

Unit 4 Review Day

Quiz

•

3rd Grade

10 questions

Identify Iconic Christmas Movie Scenes

Interactive video

•

6th - 10th Grade

20 questions

Christmas Trivia

Quiz

•

6th - 8th Grade

18 questions

Kids Christmas Trivia

Quiz

•

KG - 5th Grade

Discover more resources for Mathematics

11 questions

Solve Systems of Equations and Inequalities

Quiz

•

9th - 12th Grade

17 questions

Identify Linear and Nonlinear Functions

Quiz

•

8th - 12th Grade

15 questions

Identify Triangle Congruence Postulates

Quiz

•

9th - 12th Grade

12 questions

Combine Like Terms

Quiz

•

6th - 12th Grade

20 questions

Multi-Step Equations and Variables on Both Sides

Quiz

•

9th - 12th Grade

20 questions

Multiplication and Division Facts

Quiz

•

3rd - 12th Grade

30 questions

Unit 1 Final Review

Quiz

•

9th - 12th Grade

17 questions

Triangle Congruence Theorems

Quiz

•

9th - 11th Grade