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0580/23 May/Jun 2025, Question 9: Solving Quadratics by Factorising

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 5 marks

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The question, in short

Solve the quadratic equation 5x² = 12 − 17x, then use the given integer equation ax² + a = b with one solution x = 6 to find its other solution.

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Part (a) · 4 marks

Solve 5x² = 12 − 17x for x.

  1. 15x² + 17x − 12 = 0
  2. 2(5x − 3)(x + 4) = 0
  3. 3x = 3/5 or x = −4

Answer3/5 or 0.6 and −4

Part (b) · 1 mark

Given ax² + a = b with integers a and b and one solution x = 6, write down the other solution.

  1. 1ax² = b − a, so x² = (b − a)/a and x = ±6
  2. 2Other solution x = −6

Answer−6

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Also searched as: 0580/23/M/J/25 · 0580_s25_qp_23 · 0580 s25 23 · question 9.
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