4PM1/01 Nov 2021, Question 1: Roots α and β of a Quadratic
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 7 marks
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The question, in short
Given roots α and β of 4x² − 3x − 8 = 0, use relationships between coefficients and roots to construct a new quadratic with integer coefficients whose roots are 1/α and 1/β.
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Solution · 7 marks
- 1α + β = 3/4, αβ = −2
- 2Sum: 1/α + 1/β = (α + β)/(αβ) = (3/4)/(−2) = −3/8
- 3Product: 1/(αβ) = −1/2
- 4x² + (3/8)x − 1/2 = 0
- 58x² + 3x − 4 = 0
Answer8x² + 3x − 4 = 0
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