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8 marksCubic Functions and Equations

CAPE Pure Mathematics Unit 1 · May/June 2018 · Paper 2 · Question 2(c)

Given that α, β and γ are the roots of the equation 2x³ - x² + 1 = 0, determine the equation whose roots are 1/(αβ), 1/(αγ) and 1/(βγ). Note: (αβ)² + (αγ)² + (βγ)² = (αγ + βα + γα)² – 2 αβγ(α + β + γ) α² + β² + γ² = (α + β + γ)² – 2(αβ + αγ + βγ)

Determine the equation whose roots are 1/(αβ), 1/(αγ) and 1/(βγ).

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Other parts of this question

  1. 2(a)(i)On the diagram above, sketch the inverse of f(x).[2 marks]
  2. 2(a)(ii)Use a graphical method to show that f is bijective.[3 marks]
  3. 2(b)(i)Prove that |x - y| ≤ |x - z| + |z - y| for all x, y, z ∈ R.[4 marks]
  4. 2(b)(ii)Solve the inequality |6x - 2| + x² ≤ 5.[8 marks]

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