Podcast
Questions and Answers
For which equations is the solution (-4,0)? (Select one)
For which equations is the solution (-4,0)? (Select one)
- x^2 + 4 = 0
- x^2 - 4x = 0
- x^2 + 4x = 0 (correct)
- (x + 4)^2 = 0
What is the solution set for the quadratic equation x^2 + 5x + 4 = 0?
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?
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)
For which equation is the solution set {-1, 5}? (Select one)
What is the solution set for the quadratic equation 4y^2 + 4y - 3 = 0?
What is the solution set for the quadratic equation 4y^2 + 4y - 3 = 0?
For which equation is the solution set {1/4, 1/2}? (Select one)
For which equation is the solution set {1/4, 1/2}? (Select one)
What must be added to both sides of the quadratic to solve it by completing the square in r^2 + 4r = 0?
What must be added to both sides of the quadratic to solve it by completing the square in r^2 + 4r = 0?
Can the quadratic x^2 - 5x - 6 = 0 be factored? If so, what are the factors?
Can the quadratic x^2 - 5x - 6 = 0 be factored? If so, what are the factors?
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?
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?
What must be added to both sides of the quadratic to solve it by completing the square in x^2 - 10x = 2?
What must be added to both sides of the quadratic to solve it by completing the square in x^2 - 10x = 2?
What is the PRODUCT of the solution to the equations 4x^2 - 2 = 0? Use a calculator.
What is the PRODUCT of the solution to the equations 4x^2 - 2 = 0? Use a calculator.
What is the SUM of the solutions to the equation 5x^2 + 3x - 2 = 0?
What is the SUM of the solutions to the equation 5x^2 + 3x - 2 = 0?
Simplify (3a^2b^2 + 2ab^2 - 2a^2b + 3) - (3ab^2 + ab - 3).
Simplify (3a^2b^2 + 2ab^2 - 2a^2b + 3) - (3ab^2 + ab - 3).
Simplify (xyz)(xy^2)(y^3z^2).
Simplify (xyz)(xy^2)(y^3z^2).
Simplify (3x - 2y + 2) - 2(x + 3y - 3).
Simplify (3x - 2y + 2) - 2(x + 3y - 3).
Flashcards
Solution to x² + 4x = 0
Solution to x² + 4x = 0
The value of x that satisfies the equation x² + 4x = 0, which is x = -4, 0
Solutions to x² + 5x + 4 = 0
Solutions to x² + 5x + 4 = 0
The values of x that solve the equation x² + 5x + 4 = 0, which are x = -4, -1
Solutions to x² + 8x + 4 = 0
Solutions to x² + 8x + 4 = 0
The values of x = -4 + 2√3, -4 - 2√3 which solve the equation x² + 8x + 4 = 0
Solutions to x² - 4x - 5 = 0
Solutions to x² - 4x - 5 = 0
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Solutions to 4y² + 4y - 3 = 0
Solutions to 4y² + 4y - 3 = 0
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Solutions to 8x² - 6x + 1 = 0
Solutions to 8x² - 6x + 1 = 0
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Completing the square in r² + 4r = 0
Completing the square in r² + 4r = 0
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Factoring x² - 5x - 6 = 0
Factoring x² - 5x - 6 = 0
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Completing the square in x² + 6x - 5 = 0
Completing the square in x² + 6x - 5 = 0
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Completing the square in x² - 10x = 2
Completing the square in x² - 10x = 2
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Product of solutions to 4x² - 2 = 0
Product of solutions to 4x² - 2 = 0
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Sum of solutions to 5x² + 3x - 2 = 0
Sum of solutions to 5x² + 3x - 2 = 0
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Simplify (3a²b² + 2ab² - 2a²b + 3) - (3ab² + ab - 3)
Simplify (3a²b² + 2ab² - 2a²b + 3) - (3ab² + ab - 3)
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Simplify (xyz)(xy²)(y³z²)
Simplify (xyz)(xy²)(y³z²)
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Simplify (3x - 2y + 2) - 2(x + 3y - 3)
Simplify (3x - 2y + 2) - 2(x + 3y - 3)
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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.
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