## Objectives

1. Solve quadratic equations using factorization, completing the square, and the quadratic formula
2. Recognize the relationship between the roots and coefficients of a quadratic equation
3. Understand the discriminant and its role in determining the nature of roots
4. Apply the solutions of quadratic equations in practical situations
5. Develop skills in forming and solving quadratic equations
6. Apply the knowledge of quadratic equations in real-life problem-solving scenarios
7. Understand the concept of quadratic equations

## Lesson Note

A quadratic equation is a second-order polynomial equation in a single variable x, with a non-zero coefficient for x². The general form of a quadratic equation is:

## Lesson Evaluation

Congratulations on completing the lesson on Quadratic Equations. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.

You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.

Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.

1. Factorize the quadratic equation x^2 - 5x + 6 = 0. A. (x - 2)(x - 3) B. (x + 2)(x - 3) C. (x - 2)(x + 3) D. (x + 2)(x + 3) Answer: A. (x - 2)(x - 3)
2. Solve the quadratic equation x^2 + 4x + 4 = 0 using completing the square method. A. (x + 2)^2 = 0 B. (x + 4)^2 = 0 C. (x + 1)^2 = 0 D. (x + 3)^2 = 0 Answer: A. (x + 2)^2 = 0
3. What are the roots of the quadratic equation 2x^2 - 5x - 3 = 0? A. x = 3, x = -2 B. x = -3, x = 2 C. x = 3, x = 2 D. x = -3, x = -2 Answer: A. x = 3, x = -0.5
4. If a quadratic equation has a discriminant value of 0, what can be said about its roots? A. The roots are irrational B. The equation has no real roots C. The roots are equal D. The roots are imaginary Answer: C. The roots are equal
5. Given the roots of a quadratic equation are x = -1, x = 5, what is the equation? A. x^2 - 4x - 5 = 0 B. x^2 + 4x - 5 = 0 C. x^2 + 6x - 5 = 0 D. x^2 + 6x + 5 = 0 Answer: B. x^2 + 4x - 5 = 0

## Past Questions

Wondering what past questions for this topic looks like? Here are a number of questions about Quadratic Equations from previous years

Question 1

Solve the following quadratic inequality:

Question 1

From the graph determine the roots of the equation y = 2x2 + x - 6

Practice a number of Quadratic Equations past questions