Quadratic Inequalities Worksheet
Solve the Quadratic Inequalities
1x2 − 6x + 8 > 0
2x2 + 2x +1 ≥ 0
3x2 + x +1 > 0
47x2 + 21x − 28 < 0
5 −x2 + 4x − 7 < 0
6
74x2 − 4x + 1 ≤ 0
8
9x4 − 25x2 + 144 < 0
10x4 − 16x2 − 225 ≥ 0
1
x2 − 6x + 8 > 0
x2 − 6x + 8 = 0
P(0) = 02 − 6 · 0 + 8 > 0
P(3) = 32 − 6 · 3 + 8 = 17 − 18 < 0
P(5) = 52 − 6 · 5 + 8 = 33 − 30 > 0
S = (-∞, 2) (4, ∞)
2
x2 + 2x +1 = 0
(x + 1)2 ≥ 0
As a number squared is always positive.
S = 
3
x2 + x +1 > 0
x2 + x +1 = 0
P(0) = 0 + 0 + 1 > 0
The sign obtained coincides with the inequality, the solution is .
4
7x2 + 21x − 28 < 0
x2 +3x − 4 < 0
x2 +3x − 4 = 0
P(−6) = (−6)2 +3 · (−6)− 4 > 0
P(0) = 02 +3 · 0 − 4 < 0
P(3) = 32 +3 · 3 − 4 > 0
(−4, 1)
5
−x2 + 4x − 7 < 0
x2 − 4x + 7 = 0
P(0) = −02 + 4 ·0 − 7 < 0
S =
6
P(−3) = 4 · (−3)2 − 16 > 0
P(0) = 4 · 0 2 − 16 < 0
P(3) = 4 · 3 2 − 16 > 0
(-∞ , −2] 
[2, +∞)
7
4x2 − 4x + 1 ≤ 0
4x2 − 4x + 1 = 0
8
The first factor is always positive.
P(−17) = (−17) 2 + 12 · 17 − 64 > 0
P(0) = 02 + 12 · 0 − 64 < 0
P(5) = 5 2 + 12 · 5 − 64 > 0
(-∞, −16] [4, ∞)
9
x4 − 25x2 + 144 < 0
x4 − 25x2 + 144 = 0
(−4, −3) (−3, 3 ) (3, 4) .
10
x4 − 16x2 − 225 ≥ 0
x4 − 16x2 − 225 = 0
(x2 - 25) · (x2 + 9) ≥ 0
The second factor is always positive and different to 0.
(x2 − 25) ≥ 0
(-∞, −5] [5, +∞)
