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4PM1/02 Jan 2020, Question 5: 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 α + β = 7/2 and αβ = 2, form two quadratics with integer coefficients: one with roots α and β, another with roots α/β and β/α.

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Part (a) · 2 marks

Form a quadratic equation with integer coefficients whose roots are α and β, using the given sum and product.

  1. 1x² − (sum)x + (product) = 0
  2. 2x² − (7/2)x + 2 = 0
  3. 32x² − 7x + 4 = 0

Answer2x² − 7x + 4 = 0

Part (b) · 6 marks

Form a quadratic equation with integer coefficients whose roots are α/β and β/α.

  1. 1Product of new roots = (α/β)(β/α) = 1
  2. 2Sum = (α² + β²)/(αβ) = ((α + β)² − 2αβ)/(αβ)
  3. 3= (49/4 − 4)/2 = 33/8
  4. 4x² − (33/8)x + 1 = 0
  5. 58x² − 33x + 8 = 0

Answer8x² − 33x + 8 = 0

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