Page 79 - Mathematics_Form_Two

Algebra

Solving quadratic equations by Solution
factorization 3x 2 x - = 0.
To solve quadratic equations by x (3x - 1) = 0
factorisation, the following steps can be Either, x = or 3x −=
1 0.
0
used: 1
FOR ONLINE READING ONLY
0
1. Write the equation in standard form: Therefore, x = or x = 3 .
2
ax + bx c+= 0.
2 Rewrite the quadratic expression Example 4�27
ax + 2 bx c+ as a product of two Solve the quadratic equation Mathematics for Secondary Schools
linear factors. 10x + 9x += 0.
2
2
3. Set each factor equal to zero and
solve for x. Solution
2
From 10x + 9x += 0, it implies that
2
Note: a = 10, b = 9, c = . It follows that
2
If a quadratic equation is expressed
as a product of two linear factors, say ac = 10 2´ = 20 .
(x+ a)(x+b) = 0, where a and b are Factors of ac = 20 are 1, 2, 4, 5, 10, 20.
constants, then x+ a = 0 or x+b= 0
or both factors are equal to zero. This is Among the factors, 4 and 5 give a product
called Zero factor theorem which states of 20 and a sum of 9.
that, if a product of two or more factors Now, use 4 and 5 to split the middle term:
is zero, then at least one of the factors 2
2 0
must be zero. 10x + 5x + 4x +=
5 (2 x ) 1x ( 2 ++ 2 + ) 1x 0 =
Example 4�25 (2x 15x + )( + ) 2 = 0
Either 2x + 1 = 0 or 5x + 2 = 0.
Solve the equation (x + 4)(x – 3) = 0.
1 2
Solution Therefore, x = - 2 or x = - 5 .
If (x + 4)(x – 3) = 0, then either
x + 4 = 0 or x – 3 = 0. Example 4�28

Therefore, x = – 4 or x = 3.
2
Solve for t if t + 6t +=
8 0.
Example 4�26 Solution
8
2
Given t + 6t += 0. Split the middle
Solve the quadratic equation term to get,
3x 2 x - = 0.
t + 2 4t + 2t + 8 0.=

73
Student's Book Form Two

11/10/2024 20:11:57
MATHEMATIC F2 v5.indd 73 11/10/2024 20:11:57
MATHEMATIC F2 v5.indd 73