← Back to the activity

Year 9 Maths — Quadratic equations

Solve quadratic equations by factorising, and use the discriminant to describe the roots.

Name: ________________________

  1. 1.For x² - 7x + 10 = 0, what is the sum of the two roots?

  2. 2.Solve x² + 7x + 12 = 0. Give the smaller root.

  3. 3.What is the discriminant, b² - 4ac, of x² - 3x + 5 = 0?

  4. 4.Solve x² - 5x + 6 = 0. Give the smaller root.

  5. 5.For x² - 7x + 10 = 0, what is the product of the two roots?

  6. 6.Solve x² - 4x - 5 = 0. Give the positive root.

  7. 7.Match each quadratic to its factorised form.

    • x² + 5x + 6
    • x² - 5x + 6
    • x² - 4
    • x² + 4x + 4
    • (x + 2)(x + 3)
    • (x + 2)(x + 2)
    • (x + 2)(x - 2)
    • (x - 2)(x - 3)

  8. 8.Solve x² - 5x + 6 = 0. Give the larger root.

Answer key — Year 9 Maths — Quadratic equations

  1. 1. 7
  2. 2. -4
  3. 3. -11
  4. 4. 2
  5. 5. 10
  6. 6. 5
  7. 7. x² + 5x + 6 → (x + 2)(x + 3); x² - 5x + 6 → (x - 2)(x - 3); x² - 4 → (x + 2)(x - 2); x² + 4x + 4 → (x + 2)(x + 2)
  8. 8. 3