Successfully reported this slideshow.
Upcoming SlideShare
×

1,547 views

Published on

• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

1. 1. Quadratic Equations 2.4 To Form Quadratic Equations From Given Roots 2.1 Recognising Quadratic Equations 2.2 The ROOTs of a Quadratic Equation (Q.E) 2.3 To Solve Quadratic Equations 2.5 Relationship between and the roots of Q.E
2. 2. 2.1 Recognising Quadratic Equations Students will be taught to 1. Understand the concept quadratic equations and its roots. Learningt Outcomes Learningt Objectives Students will be able to: 1.1 Recognise quadratic equation and express it in general form
3. 3. QUADRATIC EQUATIONS (ii) Characteristics of a quadratic equation: (a) Involves only ONE variable, (c) The highest power of the variable is 2. (i) The general form of a quadratic equation is ; a, b, c are constants and a ≠ 0. (b) Has an equal sign “ = ” and can be expressed in the form ,
4. 4. 2.1 Recognising Quadratic Equations Exercise Module Q.E page1
5. 5. Students will be taught to 2. Understand the concept of quadratic equations. Learningt Outcomes Learningt Objectives Students will be able to: 2.1 Determine the roots of a quadratic equation by 2.3 To Solve Quadratic Equations ( a ) Factorisation ( b ) completing the square ( c ) using the formula
6. 6. Method 1 By Factorisation This method can only be used if the quadratic expression can be factorised completely. Example: Solve the quadratic equation
7. 7. Example: Method 2 Formula a=2 , b =-8, c=7 x = 2.707 atau 1.293 Solve the quadratic equation by formula.Give your answer correct to 4 significant figures
8. 8. Method 3 By Completing The Square Example 1: Simple Case : When a = 1 - To express in the form of Solve by method of completing square
9. 9. Method 3 By Completing The Square Example 2: [a = 1, but involving fractions when completing the square] x = - 0.5616 x = 3.562 or - To express in the form of Solve by method of completing square
10. 10. Method 3 By Completing Square Example 3: If a ≠ 1 : Divide both sides by a first before you proceed with the process of ‘completing the square’. 2.707 or 1.293 - To express in the form of Solve by method of completing square
11. 11. Exercise Module Q.E page 4 Practice 3. By using formula,solve quadratic equation 2. Solve quadratic equation by method of completing the square <ul><li>Solve quadratic equation by factorisation. </li></ul>
12. 12. Students will be taught to 2. Understand the concept of quadratic equations. Learningt Outcomes Learningt Objectives Students will be able to: 2.2 Form a quadratic equation from given roots. 2.4 To Form Quadratic Equations from Given Roots
13. 13. 2.4 To Form Quadratic Equations from Given Roots If the roots of a quadratic equation are α and β, That is, x = α , x = β ; Then x – α = 0 or x – β = 0 , (x – α) ( x – β ) = 0 The quadratic equation is Sum of roots product of roots Find the quadratic equation with roots 2 dan- 4. x = 2 , x = - 4
14. 14. 2.4 To Form Quadratic Equations from Given Roots Compare Given that the roots of the quadratic equation are -3 and ½ . Find the value of p and q.
15. 15. Practice Exercise Module page 9 L2. Find the quadratic equation with roots 2 dan- 4. L1. Find the quadratic equation with roots -3 dan 5.
16. 16. Find out SOR and POR of Find out SOR and POR of
17. 17. Find SOR and POR Find SOR and POR of
18. 18. Exercise Exercise 2.2.2 (Text book Page 34) 2 (a ) (b) (c ) (d) 3 ( a) (b ) ( c) 5. 10-3-2009 Skill Practice 2 (a ) (b) (c ) (d)
19. 19. Students will be taught to 3. Understand and use the condition for quadratic equations to have Learningt Outcomes Learningt Objectives Students will be able to: ( a ) two different roots ( b ) two equal roots ( c ) no roots 2.5.1 Relationship between and the roots of Q.E 3.1 Determine types of roots of quadratic equation from the value of .
20. 20. Q.E. has two distinct/different /real roots. The Graph y = f(x) cuts the x-axis at TWO distinct points. 2.5 The Quadratic Equation 2.5.1 Relationship between and the roots of Q.E
21. 22. Q.E. has real and equal roots. The graph y = f(x) touches the x-axis [ The x-axis is the tangent to the curve] 2.5 The Quadratic Equation 2.5.1 Relationship between and the roots of Q.E
22. 24. Q.E. does not have real roots. Graph y = f(x) does not touch x-axis. Graph is above the x-axis since f(x) is always positive. Graph is below the x-axis since f(x) is always negative. 2.5 The Quadratic Equation 2.5.1 Relationship between and the roots of Q.E
23. 25. ( a) x = -6 and x=3 ( x+6 )( x-3 )=0 Comparing P = 6 q = -36 a = 2 b= 6 c=-36-k does not have real roots. The roots of quadratic equation are -6 and 3 Find (a) p and q, (b) range of values of k such that does not have real roots.
24. 26. Practice Exercise Module page 9 1. Find the range of k if the quadratic equation has real and distinct roots. 2. Find the range of p if the quadratic equation has real roots.