Quadratic inequalities

The Maths Habit

  1. Solve 5x + 3 > 18

    x > 3

  2. Solve 4x − 7 ≤ 9

    x ≤ 4

  3. Solve 2x + 11 ≥ 5

    x ≥ −3

Which numbers have
a square less than 25?

Any number between −5 and 5, negatives too

Where does the curve cross the x axis?

  1. y = (x − 1)(x − 4)

    1 and 4

  2. y = (x + 2)(x − 5)

    −2 and 5

  3. y = (x + 3)(x + 6)

    −3 and −6

  4. y = x(x − 7)

    0 and 7

Between the roots or outside them?

  1. < 0

    Between

  2. > 0

    Outside

  3. ≤ 0

    Between

  4. ≥ 0

    Outside

Solve x2 − 6x + 8 < 0

factorise(x − 2)(x − 4)24
Answer2 < x < 4

Solve x2 − x − 6 > 0

factorise(x + 2)(x − 3)−23
Answerx < −2 or x > 3

Solve x2 − 6x + 8 < 0

factorise(x − 2)(x − 4)24
Answer2 < x < 4

Solve x2 − 4 ≤ 0

factorise(x + 2)(x − 2)−22
Answer−2 ≤ x ≤ 2

Quadratic inequalities worksheet, page 1

Answer sheet

  1. Write down the integers that satisfy x2 − 2x − 3 < 0.

    0, 1, 2

  2. Solve x2 ≥ 49

    x ≤ −7 or x ≥ 7

  1. Solve x2 − 7x + 10 < 0

    2 < x < 5

  2. Solve x2 + x − 12 > 0

    x < −4 or x > 3

  3. Write down the integers that satisfy x2 + x − 6 < 0

    −2, −1, 0, 1
Exit tickets to print