Topic Algebra Subtopic Solving Quadratic Equation using Factorisation

Topic: Algebra Sub-topic: Solving Quadratic Equation using Factorisation Free Powerpoint Templates

Basic Algebra Skills Solving – find the value of x Example 1: Solve (x – 1)(x +1) = 0 x– 1=0 x=1 OR Important Concept Ax. B=0 So, A = 0, B = 0 x+1=0 x = -1 Important Concept NOT A x TRUE! B=2 So, A = 2, B = 2

Basic Algebra Skills Solving – find the value of x Example 2: Solve x(x - 2) = 0 x=0 OR x-2=0 x=2

Basic Algebra Skills Solving Quadratic Equation by Factorisation v. Quadratic Equation (ax 2 + bx + c = 0, where a, b, c are constant) Example 3: Solve 2 x 2 - 5 x - 3 = 0 Method: Factorise 2 x 1 x x -3 -6 x 2 x 2 -3 -5 x Possibilities 1 x -3 3 x -1 (2 x + 1)(x - 3) = 0 Answer: 2 x +1 = 0 OR x - 3 = 0 x = -1/2 x=3

Basic Algebra Skills Solving Quadratic Equation by Factorisation Example 4: Solve (9 x – 1)(x – 2) = -7 x – 2 Expand: 9 x² - 18 x – x + 2 = -7 x – 2 Move all terms to LHS: 9 x² - 18 x – x + 2 + 7 x + 2 = 0 Factorise: 9 x² - 17 x + 4 = 0 Method: Factorise 3 x -1 -3 x 3 x -4 -12 x 9 x 2 4 -17 x Possibilities 1 x 4 -1 x -4 2 x 2 -2 x -2 (3 x - 1)(3 x - 4) = 0 Answer: 3 x -1 = 0 OR 3 x - 4 = 0 x = 1/3 x = 4/3

Topic: Algebra Sub-topic: Solving Quadratic Equation using Completing Square Free Powerpoint Templates Page 6

Quadratic Equation ax 2 + bx + c = 0 where a, b, c are constant Completing Square method: Formula: Steps: 1. Shift c to other side of the equation 2. Change the coefficient of x² to 1 (divide by a) 3. Add (coefficient of x)² to both side of the equation 2 Free Powerpoint Templates 4. Factorise and simplify the equation Page 7

Example 1: Solve the equation x² + 6 x + 4 = 0, by completing the square method, giving answer to 3 sig fig Coefficient of x = 6 Ans: Free Powerpoint Templates Page 8 x = -5. 24 or x = -0. 764

Example 2: Solve the equation x² - x - 3 = 0, by completing the square method, giving you answer to 3 sig fig Coefficient of x = -1 Ans: Free Powerpoint Templates Page 9 x = -1. 30 Or x= 2. 30

Example 3: Solve the equation 2 x² + 9 x - 5 = 0, by completing the square method, giving your answer to 3 sig fig Remove 2 by dividing the equation by 2 Coefficient of x = 9/2 Free Powerpoint Templates Page 10

Example 3: Solve the equation 2 x² + 9 x - 5 = 0, by completing the square method Ans: x = -5 Or x = 0. 5 Free Powerpoint Templates Page 11

Exercise: Solve using completing square method: (giving your answer to 3 sig fig) 1. 2. 3. 4. 5. 6. Free Powerpoint Templates Page 12

TOPIC: ALGEBRA Sub-topic: SOLVING QUADRATIC EQUATION using Formula Powerpoint Templates Page 13

Quadratic Equation ax 2 + bx + c = 0 where a, b, c are constant Quadratic Formula: Powerpoint Templates Page 14

Example 1 Solve the equation x² + 6 x + 4 = 0, by using quadratic formula, giving answer to 3 sig fig x² + 6 x +4 = 0 a=1 b=6 c=4 The equation has real roots Powerpoint Templates Page 15

Example 2 Solve the equation 4 x² + 20 x + 25 = 0, by using quadratic formula, giving answer to 3 sig fig 4 x² + 20 x + 25 = 0 a=4 b = 20 c = 25 The equation has equal real roots Powerpoint Templates Page 16

Example 3 Solve the equation 2 x² - 3 x + 7 = 0, by using quadratic formula, giving answer to 3 sig fig 2 x² - 3 x + 7 = 0 a=2 b = -3 c=7 The equation has no real roots Powerpoint Templates Page 17

Exercise Solve using quadratic formula: (giving your answer to 3 sig fig) 1. 2. 3. 4. 5. Powerpoint Templates Page 18