Page 84 - Mathematics_Form_Two

Algebra

Solution
5 17 5 17
Therefore, x or = - . 2
or x = +
2 2 2 2 Given 2x +7x +6 = 0.
5 17 5 17
x or x = + = - . Divide each term by 2.
2 2 2 2 7
FOR ONLINE READING ONLY
3
x + 2 x += 0.
2
Mathematics for Secondary Schools Solve the quadratic equation Subtract 3 from both sides,

Example 4�38
7

= -
3.
by completing the
x +
2
x
7x -
2
3x
60=
-
2
square.
Solution
2
7
æö

2
7x -
Given 3x
4
èø
term by 3 to get - 60= . Divide each Add ç÷ on both sides. 2
2
7
7
7 x 2 7 x + + æö = - 3 + æö
ç÷
ç÷
x 2 x - - 20= 2 èø èø
4
4
3
7 2
x 2 x - = 2 æ 7 ö 49 - 48 49+
3 ç è x + 4 ø ÷ = - 3 + 16 = 16
7 49 49
2
x 2 x - + =+ 2
3 36 36 7 æ 1 ö
ç è x + 4 ø ÷ = 16
+
 7  2 72 49 121
 x −  = =
 6  36 36 Take the square root on both sides:
7 121 11 7 17 7 11 1 1 1
x −=  =  x + = x + x + ± == = == ±±
6 36 6 4 164 4 416 16 4 4
7 11
x = ± 7
6 6 Subtract on both sides to get
4
7 11 7 11-
+
x = or x = 7 1 - 71±
6 6 x = - ± =
2 4 4 4
3
Thus, x = or x = - .
3 7 1 - + - 3 or 7 1 -- - 8 2
2 x 4 = 2 or x = = 4 = 4 = -
Therefore, x = or x = - .
3
3 7 1 - + - 3 7 1 -- - 8
x 4 = 2 x = or = 4 = 4 = - 2
Example 4�39
33
Solve the quadratic equation Therefore, x x or x = - or x = - or = - = 2. 2.-
22
2
6
2x + 7x + = 0.
78
Student's Book Form Two
11/10/2024 20:12:03
MATHEMATIC F2 v5.indd 78 11/10/2024 20:12:03
MATHEMATIC F2 v5.indd 78