SOLVING QUADRATIC INEQUALITIES ALGEBRAICALLY PRACTICE QUESTIONS

Solve the following quadratic inequalities

1)  2x2 + x − 15 ≤ 0

2)  −x2 + 3x − 2 ≥ 0

Solution

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

Solution

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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