0580/41 May/Jun 2025, Question 18: The Quadratic Formula and Completing the Square
Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 3 marks
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The question, in short
Rewrite the quadratic 2x² + 12x − 2 in completed-square form a(x + b)² − c and determine the constants a, b and c.
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Solution · 3 marks
- 12x² + 12x − 2 = 2(x² + 6x) − 2
- 2= 2[(x + 3)² − 9] − 2
- 3= 2(x + 3)² − 20
- 4a = 2, b = 3, c = 20
Answera = 2, b = 3, c = 20
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