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Worksheet by Kuta Software LLC
Algebra 1X - Quadratic Equations Name___________________________________
Period____Date________________
©
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Unit 11 Review
Find the discriminant of each quadratic equation then state the number of real solutions.
1)
9
n
2
+ 6
n
+ 1 = 0 2)
−3
x
2
− 6
x
+ 9 = 0
Solve each equation by completing the square.
3)
v
2
+ 16
v
− 24 = 5 4)
b
2
− 4
b
− 37 = −7
Solve each equation by factoring.
5)
x
2
− 6
x
+ 5 = 0 6)
x
2
− 2
x
− 24 = 0
Solve each equation by taking square roots.
7)
a
2
− 10 = −10 8)
k
2
− 9 = 90
Solve each equation with the quadratic formula.
9)
11
x
2
+ 11
x
− 10 = 0 10)
4
p
2
− 6
p
− 11 = 0
11)
4
m
2
−
m
− 50 = 10 12)
8
n
2
+ 12
n
− 5 = 12
Solve each equation by taking square roots.
13)
x
2
+ 6 = 31 14) 64
r
2
= 16
Solve each equation with the quadratic formula.
15) 5
n
2
=
9
n
+ 2 16)
4
b
2
− 9 = 5
b
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Worksheet by Kuta Software LLC
Algebra 1X - Quadratic Equations Name___________________________________
Period____Date________________
©
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Unit 11 Review
Find the discriminant of each quadratic equation then state the number of real solutions.
1)
9
n
2
+ 6
n
+ 1 = 0
0; one real solution
2)
−3
x
2
− 6
x
+ 9 = 0
144; two real solutions
Solve each equation by completing the square.
3)
v
2
+ 16
v
− 24 = 5
{
−8 + 93,
−8 −
93
}
4)
b
2
− 4
b
− 37 = −7
{
2 + 34,
2 −
34
}
Solve each equation by factoring.
5)
x
2
− 6
x
+ 5 = 0
{
1, 5
}
6)
x
2
− 2
x
− 24 = 0
{
−4, 6
}
Solve each equation by taking square roots.
7)
a
2
− 10 = −10
{
0
}
8)
k
2
− 9 = 90
{
311,
−3 11
}
Solve each equation with the quadratic formula.
9)
11
x
2
+ 11
x
− 10 = 0
{
−11 + 561
22
,
−11 −
561
22
}
10)
4
p
2
− 6
p
− 11 = 0
{
3 + 53
4
,
3 −
53
4
}
11)
4
m
2
−
m
− 50 = 10
{
4,
−
15
4
}
12)
8
n
2
+ 12
n
− 5 = 12
{
−3 + 43
4
,
−3 −
43
4
}
Solve each equation by taking square roots.
13)
x
2
+ 6 = 31
{
5, −5
}
14) 64
r
2
= 16
{
1
2
,
−
1
2
}
Solve each equation with the quadratic formula.
15) 5
n
2
=
9
n
+ 2
{
2,
−
1
5
}
16)
4
b
2
− 9 = 5
b
{
9
4
, −1
}