4MA1/2H Jun 2020, Question 17: Quadratic Inequalities
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks
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The question, in short
Rectangle has width (2x − 4) cm and height (3x + 2) cm, area A cm². Given A < 3x + 27, find the range of possible x values.
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Solution · 5 marks
- 1A = (3x + 2)(2x − 4) = 6x² − 8x − 8
- 26x² − 8x − 8 < 3x + 27, so 6x² − 11x − 35 < 0
- 3(2x − 7)(3x + 5) < 0, so −5/3 < x < 7/2
- 4The width must be positive: 2x − 4 > 0, so x > 2
- 52 < x < 7/2
Answer2 < x < 7/2
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