Page 86 - Mathematics_Form_Two

Algebra

- b+ b - 4 -- b - 4ac ac 1 3
2
2
b
or x = −
; where a
Therefore, x or = Therefore, x = - 3 ¹ 0. 2 .
or x =
2 2a a
b
- b+ b - 4 -- b - 4ac ac
2
2
x or x = = ; where a ¹ 0. Example 4�41
2a
a
2 If ax + bx c+= 0; where a ≠ 0, then Solve 5x − 6x −= using the
FOR ONLINE READING ONLY
2
10
2
Mathematics for Secondary Schools formula. 2a 2 4ac provided that Solution 2 6x −= , then a = 5,
quadratic formula.
−
b −
b
x =
10
Given 5x −
4ac is the general quadratic
2
b 
b=−6 and c =−1.
Example 4�40 By using the quadratic formula,
2
− b − 4ac
b
Solve 6x + 11x += x = 2a
2
3 0 using the
quadratic formula.
2
−− ( ) 6 −  ( ) 1
−
45−
( ) 6 
Solution x =
2 5

Comparing ax + bx c+= 0 with 6 ± 36 20+ 6 ± 56
2
2
3 0
6x + 11x += gives, a = 6, b=11, x = 10 = 10
and c = 3.
6 + 56 6 − 56
Substitute these values into the Either, x = 10 or x = 10
b
2
− b − 4ac
quadratic formula x = .
2a Therefore, x = 3+ 14 or x = 3− 14 .
5 5
2
- 11± (11) - 4 6 3´´
x =
26´ Example 4�42
− 11 121 72 Solve the quadratic equation
−
x =
12 − 400k + 2 317k − 60 0= by using the
- 11± 49 quadratic formula.
x =
12
±
- 11 7 Solution
= Given 400k− 2 + 317k − 60 0= .
12
4 18 Compare the given quadratic equation
x = - or x = - .
12 12 with the standard form ax + bx c+= 0,
2
80
Student's Book Form Two
11/10/2024 20:12:06
MATHEMATIC F2 v5.indd 80
MATHEMATIC F2 v5.indd 80 11/10/2024 20:12:06