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Grade 9 Math — Quadratic equations

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

Name: ________________________

  1. 1.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

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

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

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

  5. 5.Solve x² - 9 = 0. Give the positive root.

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

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

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

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

Answer key — Grade 9 Math — Quadratic equations

  1. 1. c) two equal real roots
  2. 2. -4
  3. 3. 2
  4. 4. -11
  5. 5. 3
  6. 6. 5
  7. 7. 10
  8. 8. c) x² - 4x + 3 = 0