Solving Quadratics By Factoring Worksheet - Chapter 14-1 Page 5
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Chapter 14
Quadratic Equations
◆◆◆
Example 10:
Write the quadratic equation that has the roots x
2 and x
5.
Solution:
If the roots are 2 and
5, we know that the factors of the equation must be (x
2)
and (x
5). So
(x
2)(x
5)
0
Multiplying gives us
x
2
5x
2x
10
0
So
x
2
3x
10
0
is the original equation.
◆◆◆
Solving Radical Equations
In Chapter 13 we solved simple radical equations. We isolated a radical on one side of the
equation and then squared both sides. Here we solve equations in which this squaring operation
results in a quadratic equation.
◆◆◆
Example 11:
Solve for x:
4
3 x
1
4
x
1
x
Solution:
We clear fractions by multiplying through by
1 .
3(x
1)
4
4 x
1
x
3x
7
4
1
Squaring both sides yields
2
9x
42x
49
16(x
1)
Removing parentheses and collecting terms gives
2
9x
58x
65
0
Factoring gives
(x
5)(9x
13)
0
13
x
5 and x
9
Check:
When x
5,
4
3 5
1
4
5
1
4
3(2)
4 (checks)
2
13
When x
,
9
13
4
2
1
9
9
3
So
Remember that the squaring
2
4
operation sometimes gives an
3 •
4
extraneous root that will not
3
2
check.
3
2
6
4 (does not check)
Our solution is then x
5.
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