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8 marksCubic Functions and Equations

CAPE Pure Mathematics Unit 1 · May/June 2017 · Paper 2 · Question 2(c)

Given that α, β and γ are the roots of the equation x³ + 3x + 2 = 0, form an equation whose roots are βγ, αγ and αβ.

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Other parts of this question

  1. 2(a)(i)Given that a² + b² = 14ab, prove that ln((a+b)/4) = (1/2)(ln a + ln b).[5 marks]
  2. 2(a)(ii)Solve the equation 2ˣ + 3(2⁻ˣ) = 4. [Your response may be expressed in terms of logarithms.][6 marks]
  3. 2(b)(i)On the diagram, insert the asymptotes for the function f.[2 marks]
  4. 2(b)(ii)sketch the graph of f⁻¹, the inverse of f showing the asymptotes for f⁻¹.[4 marks]

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