0580/22 Feb/Mar 2024, Question 24: The Quadratic Formula and Completing the Square
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 2 marks
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The question, in short
Express x² − 16x + a as (x + b)² and determine the numbers a and b.
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Solution · 2 marks
- 1Expand: (x + b)² = x² + 2bx + b²
- 2Match the x terms: 2b = −16, so b = −8.
- 3Match the numbers: a = b² = (−8)² = 64
- 4a = 64, b = −8
Answera = 64, b = −8
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