4024/12 May/Jun 2021, Question 25: Algebraic Fractions
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks
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The question, in short
Given that (2x² − 5x + a)/(x² − 16) simplifies to (2x + b)/(x + 4), find the values of the constants a and b.
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Solution · 3 marks
- 1x² − 16 = (x + 4)(x − 4)
- 2So 2x² − 5x + a = (2x + b)(x − 4) = 2x² + (b − 8)x − 4b
- 3b − 8 = −5, so b = 3
- 4a = −4b = −12
- 5a = −12, b = 3
Answera = −12, b = 3
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Also searched as: 4024/12/M/J/21 · 4024_s21_qp_12 · 4024 s21 12 · question 25.
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