0606/11 May/Jun 2025, Question 7: Solving Cubic Equations
Cambridge IGCSE Additional Mathematics 0606 · Paper 11 (Non-calculator) · Non-calculator · 6 marks
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The question, in short
Find the x-coordinates where the curve y = (2x − 9)(x² + 5) + 42 crosses the x-axis, without using accurate drawing.
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Solution · 6 marks
- 12x³ − 9x² + 10x − 45 + 42 = 0, so 2x³ − 9x² + 10x − 3 = 0
- 2x = 1: 2 − 9 + 10 − 3 = 0, so (x − 1) is a factor
- 32x³ − 9x² + 10x − 3 = (x − 1)(2x² − 7x + 3)
- 42x² − 7x + 3 = (2x − 1)(x − 3)
- 5x = 1/2, 1, 3
Answerx = 1/2, 1, 3
Stuck on a step? Read the free lesson: Solving Cubic Equations
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Also searched as: 0606/11/M/J/25 · 0606_s25_qp_11 · 0606 s25 11 · question 7.
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