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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
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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
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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 ,
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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
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Method 1 By Factorisation This method can only be used if the quadratic expression can be factorised completely. Example: Solve the quadratic equation
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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
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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
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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
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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
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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>
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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
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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
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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.
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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.
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Find out SOR and POR of Find out SOR and POR of
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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)
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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 .
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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
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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
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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
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( 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.
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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.
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