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}
  9. 9. Test your power!!!! <ul><li>Solve the equation </li></ul>Answer:{1.781, -0.281}
  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
  25. 26. Again…test your power!!!!!!!!!!!
  26. 27. HOSTEL/WEEKEND JOBS
  27. 28. INEQUALITIES Objectives: <ul><li>Relate the properties of inequalities </li></ul><ul><li>Define and solve linear inequalities </li></ul><ul><li>Define quadratic inequalities and solve them using graphical method </li></ul><ul><li>Solve the quadratic by using analytical method: </li></ul><ul><li>(i) Basic definition </li></ul><ul><li>(ii) Real number line </li></ul><ul><li>(iii) Table of signs. </li></ul><ul><li>Understand and solve rational inequalities involving linear and </li></ul><ul><li>quadratic expressions. </li></ul>
  28. 29. LINEAR INEQUALITIES

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