Quadratic Equations Methods Quiz

Questions and Answers

What are the solutions to the equation $x^2 + 12x + 35 = 0$?

x = -3; x = -4

x = -5; x = -7 (correct)

x = -11; x = 7

x = 5; x = -6

What are the solutions to the equation $x^2 + 4x - 77 = 0$?

x = -11; x = 7 (correct)

x = -2; x = 3

x = 1/3; x = -1.5

x = 5; x = -6

What are the solutions to the equation $x^2 + 7x + 12 = 0$?

x = 0; x = 7

x = 1; x = -9

x = 3; x = 5

x = -3; x = -4 (correct)

What are the solutions to the equation $x^2 + x - 30 = 0$?

x = 5; x = -6 Signup and view all the answers

What are the solutions to the equation $2x^2 - 2x - 12 = 0$?

x = -2; x = 3 Signup and view all the answers

What are the solutions to the equation $x^2 - 16x - 17 = 0$?

x = 17; x = -1 Signup and view all the answers

What is the solution to the equation $x^2 - 16x + 64 = 0$?

x = 8 Signup and view all the answers

What is the solution to the equation $x^2 + 14x + 49 = 0$?

x = 7 Signup and view all the answers

What are the solutions to the equation $x^2 - 64 = 0$?

x = 8; x = -8 Signup and view all the answers

What are the solutions to the equation $x^2 + 4x - 60 = 0$?

x = 6; x = -10 Signup and view all the answers

What are the solutions to the equation $6x^2 + 7x - 3 = 0$?

x = 1/3; x = -1.5 Signup and view all the answers

What are the solutions to the equation $5x^2 - 45 = 0$?

x = 3; x = -3 Signup and view all the answers

What are the solutions to the equation $x^2 - 3x - 4 = 0$?

x = -1; x = 4 Signup and view all the answers

What are the solutions to the equation $x^2 - 8x + 15 = 0$?

x = 3; x = 5 Signup and view all the answers

What are the solutions to the equation $x^2 - 7x = 0$?

x = 0; x = 7 Signup and view all the answers

What are the solutions to the equation $(x + 4)^2 = 25$?

x = 1; x = -9 Signup and view all the answers

What are the solutions to the equation $(x - 3)^2 = 64$?

x = 11; x = -5 Signup and view all the answers

What are the solutions to the equation $5x^2 - 10x - 120 = 0$?

x = 6; x = -4 Signup and view all the answers

What are the solutions to the equation $7x^2 + 14x - 21 = 0$?

x = 1; x = -3 Signup and view all the answers

What are the solutions to the equation $x^2 - 17 = 8$?

x = -5; x = 5 Signup and view all the answers

Study Notes

Key Methods for Solving Quadratic Equations

Factoring: A common method where the equation is expressed as a product of binomials.
- Example: x² + 12x + 35 = 0 yields solutions x = -5 and x = -7.
- x² + 7x + 12 = 0 yields x = -3 and x = -4.
- x² + 4x - 60 = 0 yields x = 6 and x = -10.
- x² - 3x - 4 = 0 yields x = -1 and x = 4.
Completing the Square: Transforming the quadratic into a perfect square trinomial.
- Example: x² + 4x - 77 = 0 results in x = -11 and x = 7.
- 2x² - 2x - 12 = 0 leads to x = -2 and x = 3.
- x² - 8x + 15 = 0 gives x = 3 and x = 5.
- 7x² + 14x - 21 = 0 provides roots x = 1 and x = -3.
Quadratic Formula: A formula that provides the roots of any quadratic equation of the form ax² + bx + c = 0.
- Example: x² + x - 30 = 0 results in x = 5 and x = -6.
- 6x² + 7x - 3 = 0 yields x = 1/3 and x = -1.5.
- 5x² - 10x - 120 = 0 results in x = 6 and x = -4.
- x² - 7x = 0 gives the solutions x = 0 and x = 7.
Using Square Roots: Applies when the quadratic can be rewritten in the form (x ± a)² = b.
- Example: x² - 64 = 0 leads to x = 8 and x = -8.
- (x + 4)² = 25 results in x = 1 and x = -9.
- (x - 3)² = 64 provides roots x = 11 and x = -5.
- x² - 17 = 8 results in x = -5 and x = 5.

Summary

Various methods exist to solve quadratic equations: factoring, completing the square, quadratic formula, and using square roots.
Each method is effective depending on the specific form of the quadratic equation.
Solutions can yield rational or irrational numbers, impacting the approach chosen for solving.

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Description

Test your understanding of key methods for solving quadratic equations including factoring, completing the square, and using the quadratic formula. This quiz will challenge you with examples and require you to identify the correct solutions for various equations.