Solve the following quadratic inequalities
1) 2x2 + x − 15 ≤ 0
2) −x2 + 3x − 2 ≥ 0
3) 3x2 ≤ 12
4) x2 – 4x + 4 < 0
5) 2x2 + 7x < -6
6) x2 ≤ x + 2
7) 3x2- 6x + 3 > 0
8) 2x2 – 5 ≤ 3x
9) 3x2 ≥ 2(x + 4)
10) 6(x2 + 2) < 17x
11) 9x2 ≤ 12x - 4
12) 4 < 5x2 + 8x
Answers :
1) Possible values of x : -3 ≤ x ≤ 5/2
Interval notation : [-3, 5/2]
2) Possible values of x : 1 ≤ x ≤ 2
Interval notation : [1, 2]
3) Possible values of x : -2 ≤ x ≤ 2
Interval notation : [-2, 2]
4) All the real values.
5) Possible values of x : -2 < x < -3/2
Interval notation : (-2, -3/2)
6) Possible values of x : -1 ≤ x ≤ 2
Interval notation : [-1, 2]
7) All the real values.
8) Possible values of x : -1 ≤ x ≤ 5/2
Interval notation : [-1, 5/2]
9) Possible values of x : x ≤ -4/3 or x ≥ 2
Interval notation : (-∞, -4/3] u [2, ∞)
10) Possible values of x : 4/3 < x < 3/2
Interval notation : (4/3, 3/2)
11) Possible value of x : 2/3
12) Possible values of x : x < -2 or x > 2/5
Interval notation : (-∞, -2) u (2/5, ∞)
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