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4024/11 Oct/Nov 2022, Question 22: The Quadratic Formula and Completing the Square

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Complete the square for x² − 6x − 7 to find a and b, then use the result to solve x² − 6x − 7 = 0.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Find the values of a and b in x² − 6x − 7 = (x + a)² + b.

  1. 1Half of −6 is −3, so use (x − 3)²
  2. 2(x − 3)² = x² − 6x + 9
  3. 3x² − 6x − 7 = (x − 3)² − 9 − 7 = (x − 3)² − 16
  4. 4So a = −3, b = −16

Answera = −3, b = −16

Part (b) · 2 marks

Using your completed square, solve x² − 6x − 7 = 0, showing working.

  1. 1(x − 3)² = 16 → x − 3 = ±4
  2. 2x = 7 or x = −1

Answer7 and −1

Stuck on a step? Read the free lesson: The Quadratic Formula and Completing the Square

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Also searched as: 4024/11/O/N/22 · 4024_w22_qp_11 · 4024 w22 11 · question 22.
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