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
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