4PM1/02 Jun 2024, Question 2: Roots α and β of a Quadratic
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 8 marks
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The question, in short
Given 3x² − 5x + 1 = 0 with roots α and β, form without solving a quadratic with integer coefficients having roots α/(2β) and β/(2α).
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Solution · 8 marks
- 1α + β = 5/3, αβ = 1/3
- 2α² + β² = (α + β)² − 2αβ = 25/9 − 2/3 = 19/9
- 3Product of new roots = αβ/(4αβ) = 1/4
- 4Sum of new roots = (α² + β²)/(2αβ) = (19/9)/(2/3) = 19/6
- 5x² − (19/6)x + 1/4 = 0
- 612x² − 38x + 3 = 0
Answer12x² − 38x + 3 = 0
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