1. Quadratic Equations

2. Quadratic Equations
If ab = 0 then either a = 0 or b = 0

3. Quadratic Equations
If ab = 0 then either a = 0 or b = 0
e.g. (i ) x 2  9 x  18  0

4. Quadratic Equations
If ab = 0 then either a = 0 or b = 0
e.g. (i ) x 2  9 x  18  0
 x  6  x  3  0
x  6 or x  3

5. Quadratic Equations
If ab = 0 then either a = 0 or b = 0
e.g. (i ) x 2  9 x  18  0
 x  6  x  3  0
x  6 or x  3
(ii ) x  2 x  1  0

6. Quadratic Equations
If ab = 0 then either a = 0 or b = 0
e.g. (i ) x 2  9 x  18  0
 x  6  x  3  0
x  6 or x  3
(ii ) x  2 x  1  0
1
x  0 or x  
2

7. Quadratic Formula

8. Quadratic Formula
b  b 2  4ac
x
2a

9. Quadratic Formula
b  b 2  4ac
x
2a
e.g.(i ) 2 x 2  5 x  4  0

10. Quadratic Formula
b  b 2  4ac
x
2a
e.g.(i ) 2 x 2  5 x  4  0
5  25  32
x
4

11. Quadratic Formula
b  b 2  4ac
x
2a
e.g.(i ) 2 x 2  5 x  4  0
5  25  32
x
4
5  57 exact
x
4

12. Quadratic Formula
b  b 2  4ac
x
2a
e.g.(i ) 2 x 2  5 x  4  0
5  25  32
x
4
5  57 exact
x
4
x  3.14 or x  0.64 approximate

13. Quadratic Formula
b  b 2  4ac
x
2a
e.g.(i ) 2 x 2  5 x  4  0
(ii ) make x the subject in
5  25  32
x y  x2  4 x  3
4
5  57 exact
x
4
x  3.14 or x  0.64 approximate

14. Quadratic Formula
b  b 2  4ac
x
2a
e.g.(i ) 2 x 2  5 x  4  0
(ii ) make x the subject in
5  25  32
x y  x2  4 x  3
4
x2  4 x  3  y   0
5  57 exact
x
4
x  3.14 or x  0.64 approximate

15. Quadratic Formula
b  b 2  4ac
x
2a
e.g.(i ) 2 x 2  5 x  4  0
(ii ) make x the subject in
5  25  32
x y  x2  4 x  3
4
x2  4 x  3  y   0
5  57 exact
x
4 4  16  4  3  y 
x  3.14 or x  0.64 x
approximate 2

16. Quadratic Formula
b  b 2  4ac
x
2a
e.g.(i ) 2 x 2  5 x  4  0
(ii ) make x the subject in
5  25  32
x y  x2  4 x  3
4
x2  4 x  3  y   0
5  57 exact
x
4 4  16  4  3  y 
x  3.14 or x  0.64 x
approximate 2
4  2 4   3  y 
x
2

17. Quadratic Formula
b  b 2  4ac
x
2a
e.g.(i ) 2 x 2  5 x  4  0
(ii ) make x the subject in
5  25  32
x y  x2  4 x  3
4
x2  4 x  3  y   0
5  57 exact
x
4 4  16  4  3  y 
x  3.14 or x  0.64 x
approximate 2
4  2 4   3  y 
x
2
4  2 7  y
x
2
x  2  7  y

18. Quadratic Formula
b  b 2  4ac
x
2a
e.g.(i ) 2 x 2  5 x  4  0
(ii ) make x the subject in
5  25  32
x y  x2  4 x  3
4
x2  4 x  3  y   0
5  57 exact
x
4 4  16  4  3  y 
x  3.14 or x  0.64 x
approximate 2
4  2 4   3  y 
x
Exercise 1G; 1ad, 2ah, 3aei, 4dhl, 2
5bgl, 6bf, 7ace, 8c, 9a, 10b, 4  2 7  y
x
11aceg, 12bc, 13b* 2
x  2  7  y