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0580/21 May/Jun 2022, Question 23: The Quadratic Formula and Completing the Square

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 4 marks

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The question, in short

Complete the square on x² + 8x + 10 to find p and q, then use it to solve x² + 8x + 10 = 30.

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Part (a) · 2 marks

Find the values of p and q in the completed-square form (x + p)² + q.

  1. 1x² + 8x + 10 = (x + 4)² − 16 + 10
  2. 2= (x + 4)² − 6
  3. 3p = 4, q = −6

Answerp = 4, q = −6

Part (b) · 2 marks

Solve x² + 8x + 10 = 30.

  1. 1(x + 4)² − 6 = 30, so (x + 4)² = 36
  2. 2x + 4 = ±6
  3. 3x = 2 or x = −10

Answer−10 and 2

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Also searched as: 0580/21/M/J/22 · 0580_s22_qp_21 · 0580 s22 21 · question 23.
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