Algebra 2
Name___________________________________ ID: 1
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Solving Quadratic Inequalities
Date________________ Period____
Directions: Write legibly. Show work. Box answers. No credit will be given for answers only.
Solve each equation by factoring.
1) n 2 + 5n + 4 > -2
2) m 2 < -3m + 10
3) 15r 2 - 50r - 40 > 0
4) 17n 2 - 38 < 5n 2 + 2 - 4n
Solve each equation by taking square roots.
5) 25n 2 + 5 > 69
6) 4 x 2 - 4 < 32
Find the discriminant of each quadratic equation then state the number and type of solutions.
7) x 2 - 9 x = -8
8) -5k 2 - 10k - 3 = 2
9) 4v 2 + v + 2 = 7
10) -5 p 2 - 1 = 8
Solve each equation with the quadratic formula.
11) 3 x 2 + 3 x > 4
12) 5 x 2 - 7 < -3 x
13) 7a 2 + 4 > 7a
14) -12 p < 1 - 7 p 2
15) 8n 2 > -3
16) 4 x 2 + 10 < 7 x
Worksheet by Kuta Software LLC
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Algebra 2
Name___________________________________ ID: 1
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Solving Quadratic Inequalities
Date________________ Period____
Directions: Write legibly. Show work. Box answers. No credit will be given for answers only.
Solve each equation by factoring.
1) n 2 + 5n + 4 > -2
2) m 2 < -3m + 10 {-5, 2}
{-3, -2}
3) 15r 2 - 50r - 40 > 0
4) 17n 2 - 38 < 5n 2 + 2 - 4n
5
3
2
{- , 4}
3
{ , -2}
Solve each equation by taking square roots.
5) 25n 2 + 5 > 69
8
5
6) 4 x 2 - 4 < 32
{3, -3}
8
5
{ ,- }
Find the discriminant of each quadratic equation then state the number and type of solutions.
7) x 2 - 9 x = -8
8) -5k 2 - 10k - 3 = 2
0; one real solution
49; two real solutions
9) 4v 2 + v + 2 = 7
10) -5 p 2 - 1 = 8
-180; two imaginary solutions
81; two real solutions
Solve each equation with the quadratic formula.
11) 3 x 2 + 3 x > 4
12) 5 x 2 - 7 < -3 x
-3 + 57 -3 - 57
{
,
}
6
6
13) 7a 2 + 4 > 7a
-3 + 149 -3 - 149
,
}
10
10
14) -12 p < 1 - 7 p 2
7 + 3i 7 7 - 3i 7
{
,
}
14
14
15) 8n 2 > -3 {
{
i 6
4
,-
i 6
4
{
}
6 + 43 6 - 43
,
}
7
7
16) 4 x 2 + 10 < 7 x {
7 + i 111 7 - i 111
,
}
8
8
Worksheet by Kuta Software LLC
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