4MA1/2H Jan 2022, Question 22: Quadratic Inequalities
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks
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The question, in short
A rectangle has sides (2x + 3) cm and (x − 1) cm. Given its area is under 75 cm², find the range of possible x values.
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Solution · 5 marks
- 1Area of rectangle = (2x + 3)(x − 1)
- 2(2x + 3)(x − 1) < 75
- 32x² − 2x + 3x − 3 < 75
- 42x² + x − 3 < 75
- 52x² + x − 78 < 0
- 6(x − 6)(2x + 13) < 0
- 7Critical values: x = 6 and x = −13/2 = −6.5
- 8The expression is negative between the critical values, so −6.5 < x < 6
- 9A side length must be positive, so x − 1 > 0, giving x > 1
- 101 < x < 6
Answer1 < x < 6
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