MathClass 10Free printable

Quadratic Equations

Factorisation, the quadratic formula and nature of roots

19 questions · about 60 minutes · answer key included

Name Class Date ⭐ Score / 19

A quadratic equation has the form ax² + bx + c = 0, where a ≠ 0. It has at most two roots.

💡 Formula box

  • Quadratic formula: x = [−b ± √(b² − 4ac)] / 2a
  • Discriminant D = b² − 4ac
  • D > 0: two distinct real roots. D = 0: two equal real roots. D < 0: no real roots.

Part ASolve by factorisation

  1. x² − 5x + 6 = 0
  2. x² + x − 12 = 0
  3. 2x² − 7x + 3 = 0
  4. x² − 9 = 0
  5. 6x² − x − 2 = 0
  6. x² − 8x + 16 = 0

Part BNature of roots

Find the discriminant and say what kind of roots each equation has.

  1. 2x² − 3x + 5 = 0
  2. x² − 4x + 4 = 0
  3. 3x² + 5x − 2 = 0
  4. x² + 2x + 3 = 0
  5. 4x² − 12x + 9 = 0

Part CUse the quadratic formula

  1. x² − 4x − 1 = 0
  2. 2x² + 3x − 2 = 0
  3. x² + 6x + 4 = 0

Part DFind k

Find the value(s) of k for which each equation has two equal roots.

  1. 2x² + kx + 3 = 0
  2. kx² − 6x + 1 = 0

Part EWord problems

  1. 🔢 The product of two consecutive positive integers is 306. Find the integers.
  2. 🌾 A rectangular plot is 3 m longer than it is wide, and its area is 180 m². Find its length and breadth.
  3. 🔄 The sum of a number and its reciprocal is 10/3. Find the number.

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