Page 80 - Mathematics_Form_Two

Algebra

( tt + ) 4 ( 2 + ) 4t + 0 = Example 4�31

(t + 4)(t + 2) = 0 Solve the quadratic equation
4
9x - = 0.
2
Either t + 4 = 0 or t +2 = 0. Solution

FOR ONLINE READING ONLY
Therefore, t =−4 or t = - 2. Given 9x - 40= . It follows that
2
Mathematics for Secondary Schools Example 4�29 (3x (3 )x - 2 0 or 3x= 2 - 0 2) = 0 − 2 0.= 2 = . 0 . 0
0
2
2
2 =
(3 )x -
9x -
40=
2
2)(3x + 2
2 =
=
0 or 3x
+
either, 3 – 2x
-
(3x
0
2) =
2)(3x +
Solve the quadratic equation
2 =
+
0 or 3x
either, 3 – 2x
=
Either, 3x +

2
0.
x -
9 =
Solution
3
3
Given x - 90= . It follows that Therefore, x = - 2 or x = 2 .
2
2
x -
90=

2 2 3 x - 2 2 0 = Example 4�32
3 x - 0 =
(x 3)(x + - 3) 0= Solve the equation y 2 2y - - 24 = 0.
Solution
either (x
=
3) 0 or (x +
Either x + 3 = 0 or x – 3 = 0. - 3) 0.=
Given y y 2 2 2 2 2y - 2y -y - - - 2y - 24 = 0 0 0
24 = . It follows that
24 =
0
24 = 0 (splitting the middleterm)=
0 (splitting the middleterm)
Therefore, x = - 3 or x = 3. y y y y 2 2 2 2 2y - 6y - 6y - 6y - - 24 = - 24 0 (splitting the middleterm)
4y + 4y +
-
4y +
-
24 =
24 =
y
0(factorizing into two linear factors)
( yy - 6) 4(y-
6) 4(y+ +
( yy 6y - 6) 4(y+ 4y + - - - 6) 0 (splitting the middleterm)
6) = 0(factorizing into two linear factors)=
6) =
0(factorizing into two linear factors)
( yy -
-
6) 4(y+
6) =
-
( yy -
0(factorizing into two linear factors)
0 (by the zero factor theorem)
4) = 0 (by the zero factor theorem)=
4) =
Example 4�30 (y (y (y (y 6)(y - 6)(y - 6)(y - 6)(y - + + 4) 0 (by the zero factor theorem)
+
4) =
+
0 (by the zero factor theorem)
Solve the quadratic equation Either y – 6 = 0 or y + 4 = 0
2h 2 7h - = 39.
Therefore, y = or y = - 4.
6
Solution
Example 4�33
Given 2h 2 7h - - 39 = 0. It implies that
A rectangular garden is 6 metres wide
2h 2 6h + 13h - - 39 = 0 and 8 metres long. What length should
be added to the shorter side and reduced
2 (hh + 3) 13(h- + 3) = 0 (factorizing into twolinear factors)
from the longer side to form a rectangular
2 (hh + 3) 13(h- + 3) = 0 (factorizing into twolinear factors)
(h 3)(2h + - 13) = 0 garden with an area of 45 square metres?

0
(h 3)(2h + Either h - 13) = 3 0 or 2h += - 13 0(by the zero factor theorem)=
Either h Either 3 0 or 2h += - 13 0(by the zero factor theorem)= . Solution
Let x be the added length to the shorter
13 side. The sides of the rectangular garden
Therefore, h 3 or h = - or = .
2 will be:
13 Width =(6 + x) m and length =(8 – x) as
h 3 or = .
h = -
2 shown in the following figure.
74
Student's Book Form Two
11/10/2024 20:11:59
MATHEMATIC F2 v5.indd 74 11/10/2024 20:11:59
MATHEMATIC F2 v5.indd 74