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Year 10 Maths — Quadratic equations

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

Name: ________________________

  1. 1.Which of these is a quadratic equation?

    • a) x³ - 1 = 0
    • b) x² - 4x + 3 = 0
    • c) 2x + 5 = 0
    • d) x + 7 = 0

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

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

  4. 4.A quadratic equation whose discriminant is 0 has...

    • a) three real roots
    • b) two different real roots
    • c) two equal real roots
    • d) no real roots

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

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

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

  7. 7.The product of two consecutive whole numbers is 42. What is the smaller number?

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

Answer key — Year 10 Maths — Quadratic equations

  1. 1. b) x² - 4x + 3 = 0
  2. 2. 2
  3. 3. 3
  4. 4. c) two equal real roots
  5. 5. 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)
  6. 6. -4
  7. 7. 6
  8. 8. -11