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Mathematics

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  • 1. EQUATIONS, INEQUALITIES AND ABSOLUTE VALUE
  • 2.
    • QUADRATIC EXPRESSION AND EQUATION
    • INEQUALITIES
    • ABSOLUTE VALUES
  • 3. QUADRATIC EXPRESSION AND EQUATION
    • Objectives:
    • Define quadratic expressions and equation
    • Solve quadratic equations by factorization, completing the square methods and formula
  • 4. QUADRATIC EXPRESSION AND EQUATION Eg :
  • 5. Solving Quadratic Equations Quadratic equations can be solved by the following methods a) when can be factorized b) when cannot be factorized
  • 6. a) when can be factorized Example 1: Solve the equation Solution: Factorizing The solution set is { -2 , 3/2 }
  • 7. b) when cannot be factorized
    • completing the square
    • formula
  • 8. completing the square
    • Solve the equation
    Solution: The solution set is {1.162, -5.162}
  • 9. Test your power!!!!
    • Solve the equation
    Answer:{1.781, -0.281}
  • 10. Method using formula
  • 11. Example 3 Solution: The solution set is ????
  • 12. Test your power again !!!!
  • 13. TYPES OF ROOTS OF A QUADRATIC EQUATION
    • Objectives:
    • Recognize the type of roots based on the discriminant
    • Relate the roots
    • Form a quadratic equations using identities
  • 14. From the general equation, the types of the roots can be determined based on the value of the discriminant,
    • If
    • If
    • If
  • 15. Example Determine the nature of the roots 1. 2. 3.
  • 16. Example
  • 17. Example
  • 18. THE RELATIONSHIP BETWEEN THE ROOTS, and THE COEFFICIENTS OF A QUADRATIC EQUATION.
  • 19. In general
  • 20. Important Identities:
  • 21. Example
  • 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
  • 25. Example Given that are the roots of the quadratic equation , find quadratic equation with roots
  • 26. Again…test your power!!!!!!!!!!!
  • 27. HOSTEL/WEEKEND JOBS
  • 28. INEQUALITIES Objectives:
    • Relate the properties of inequalities
    • Define and solve linear inequalities
    • Define quadratic inequalities and solve them using graphical method
    • Solve the quadratic by using analytical method:
    • (i) Basic definition
    • (ii) Real number line
    • (iii) Table of signs.
    • Understand and solve rational inequalities involving linear and
    • quadratic expressions.
  • 29. LINEAR INEQUALITIES