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# Topic 2

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### Topic 2

1. 1. EQUATIONS, INEQUALITIES AND ABSOLUTE VALUE
2. 2. <ul><li>QUADRATIC EXPRESSION AND EQUATION </li></ul><ul><li>INEQUALITIES </li></ul><ul><li>ABSOLUTE VALUES </li></ul>
3. 3. QUADRATIC EXPRESSION AND EQUATION <ul><li>Objectives: </li></ul><ul><li>Define quadratic expressions and equation </li></ul><ul><li>Solve quadratic equations by factorization, completing the square methods and formula </li></ul>
4. 4. QUADRATIC EXPRESSION AND EQUATION Eg :
5. 5. Solving Quadratic Equations Quadratic equations can be solved by the following methods a) when can be factorized b) when cannot be factorized
6. 6. a) when can be factorized Example 1: Solve the equation Solution: Factorizing The solution set is { -2 , 3/2 }
7. 7. b) when cannot be factorized <ul><li>completing the square </li></ul><ul><li>formula </li></ul>
8. 8. completing the square <ul><li>Solve the equation </li></ul>Solution: The solution set is {1.162, -5.162}
10. 10. Method using formula
11. 11. Example 3 Solution: The solution set is ????
12. 12. Test your power again !!!!
13. 13. TYPES OF ROOTS OF A QUADRATIC EQUATION <ul><li>Objectives: </li></ul><ul><li>Recognize the type of roots based on the discriminant </li></ul><ul><li>Relate the roots </li></ul><ul><li>Form a quadratic equations using identities </li></ul>
14. 14. From the general equation, the types of the roots can be determined based on the value of the discriminant, <ul><li>If </li></ul><ul><li>If </li></ul><ul><li>If </li></ul>
15. 15. Example Determine the nature of the roots 1. 2. 3.
16. 16. Example
17. 17. Example
18. 18. THE RELATIONSHIP BETWEEN THE ROOTS, and THE COEFFICIENTS OF A QUADRATIC EQUATION.
19. 19. In general
20. 20. Important Identities:
21. 21. Example
22. 22. Solution The equation has roots Therefore,
23. 24. To find a quadratic equation given the roots, the sum and product of the roots need to be found. For example, the quadratic equation with roots 3 and 5 is
24. 25. Example Given that are the roots of the quadratic equation , find quadratic equation with roots