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High School Mathematics
6.11 Solving Quadratic Equations by Method of Factorization

Methods to solve a quadratic equation
1. The Factorization Method.
2. The Method of Solution by using Quadratic Formula.

Factorization method:

Example:
Solve, 6x2 - 13x + 6 = 0.
Solution:
We shall solve 6x2 - 13x + 6 = 0 into factors.
6x2 - 13x + 6 = 6x2 - 9x - 4x + 6
= 3x(2x - 3) - 2(2x-3)
= (3x - 2)(2x - 3)
3x - 2 = 0 and 2x - 3 = 0
Therefore, x = 2/3 or 3/2

Example:
Solve, -3m2 + 7m - 2 = 0.
Solution:
We shall solve -3m2 + 7m - 2 = 0 into factors.
-3m2 + 7m - 2 = -3m2 + 6m + 1m - 2 = 0
= 3m(-m + 2) + 1(m - 2) = 0
= 3m(-m + 2) - 1(-m + 2) = 0
= (3m - 1)(-m + 2) = 0
3m - 1 = 0 and -m + 2 = 0
Therefore, m = 1/3 or 2


Directions: Solve the following problems using factorization method. Also write at least five examples of your own.
x2 - 7 = 9
11y2 = 11
x2 + 13 = 5
3x2 - 17x + 10
49x2 - 14x + 1
Show that the roots of the quadratic equation x2 + 3x - 18 = 0 are -6 and 3
Show that the roots of the quadratic equation 2t2 - 17t + 45 = 3t - 5 is 5
Find the zeros of y = x2 - x - 6 are -2 and 3
Factor the expressions:
y = x2 - x - 2
y = 2x2 + x - 3
y = x2 + 2x + 1
Factor the trinomial:
x2 - 7x - 10
b2 + 6b - 27
r2 - 14r - 72
p2 - 5p - 6
11t2+ 14t - 16
4x2 -13x - 27
18x2 + 9x - 14
7u2 - 4u - 3

Q 1: Solve, 6x2 - 13x + 6 = 0.
2/3 and 3/2
2/3 and -3/2
-2/3 and 3/2
-2/3 and -3/2

Q 2: Solve, 6x2 + 9x - 6 = 0.
-3/2 and -2/3
3/2 and 2/3
3/2 and -2/3
-3/2 and 2/3

Q 3: Solve, 12x2 - x - 1 = 0.
1/4 and 1/3
-1/4 and -1/3
1/4 and -1/3
-1/4 and 1/3

Q 4: Solve, 6x2 + 7x + 2 = 0.
1/2 and -2/3
-1/2 and -2/3
-1/2 and 2/3
1/2 and 2/3

Q 5: Solve, 2x2 + 11x + 12 = 0.
3/2 and 4
3/2 and -4
-3/2 and -4
-3/2 and 4

Q 6: Solve, 6x2 + 13x + 5 = 0.
-5/3 and -1/2
5/3 and -1/2
5/3 and 1/2
-5/3 and 1/2

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Question 8: This question is available to subscribers only!


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