Podcast Beta
Questions and Answers
For which equations is the solution (-4,0)? (Select one)
What is the solution set for the quadratic equation x^2 + 5x + 4 = 0?
{-4, -1}
What is the solution set for the quadratic equation x^2 + 8x + 4 = 0?
{-4 + 2√3, -4 - 2√3}
For which equation is the solution set {-1, 5}? (Select one)
Signup and view all the answers
What is the solution set for the quadratic equation 4y^2 + 4y - 3 = 0?
Signup and view all the answers
For which equation is the solution set {1/4, 1/2}? (Select one)
Signup and view all the answers
What must be added to both sides of the quadratic to solve it by completing the square in r^2 + 4r = 0?
Signup and view all the answers
Can the quadratic x^2 - 5x - 6 = 0 be factored? If so, what are the factors?
Signup and view all the answers
After you have eliminated the constant on the left side of the equation, what else must be added to both sides of the quadratic to solve it by completing the square in x^2 + 6x - 5 = 0?
Signup and view all the answers
What must be added to both sides of the quadratic to solve it by completing the square in x^2 - 10x = 2?
Signup and view all the answers
What is the PRODUCT of the solution to the equations 4x^2 - 2 = 0? Use a calculator.
Signup and view all the answers
What is the SUM of the solutions to the equation 5x^2 + 3x - 2 = 0?
Signup and view all the answers
Simplify (3a^2b^2 + 2ab^2 - 2a^2b + 3) - (3ab^2 + ab - 3).
Signup and view all the answers
Simplify (xyz)(xy^2)(y^3z^2).
Signup and view all the answers
Simplify (3x - 2y + 2) - 2(x + 3y - 3).
Signup and view all the answers
Study Notes
Quadratic Equations Overview
- Solution (-4, 0) found for the equation x^2 + 4x = 0.
- The solution set for x^2 + 5x + 4 = 0 is {-4, -1}.
- The solutions for x^2 + 8x + 4 = 0 are {-4 + 2√3, -4 - 2√3}.
Factoring and Roots
- For the equation yielding solution set {-1, 5}, the correct equation is x^2 - 4x - 5 = 0.
- The solution set for 4y^2 + 4y - 3 = 0 is {-3/2, 1/2}.
- The quadratic x^2 - 5x - 6 can be factored into (x - 6)(x + 1).
Completing the Square
- To complete the square for r^2 + 4r = 0, add 4 to both sides.
- After eliminating the constant in x^2 + 6x - 5 = 0, add 9 to complete the square.
- For x^2 - 10x = 2, add 25 to both sides to complete the square.
Solutions Properties
- The product of the solutions to 4x^2 - 2 = 0 is -1/2.
- The sum of solutions for 5x^2 + 3x - 2 = 0 is -3/5.
Simplification Skills
- To simplify (3a^2b^2 + 2ab^2 - 2a^2b + 3ab) - (3ab^2 + ab - 3), the result is 3a^2b^2 - ab^2 - 2a^2b + 2ab + 3.
- The simplification of (xyz)(xy^2)(y^3z^2) results in x^2y^6z^3.
- Simplifying (3x - 2y + 2) - 2(x + 3y - 3) results in x - 8y + 8.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Prepare for your upcoming test on quadratic equations with this flashcard review. Each card presents problems related to finding solution sets for various quadratic equations, helping you strengthen your understanding and problem-solving skills.
