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8 marksCubic Functions and Equations

CAPE Pure Mathematics Unit 1 · May/June 2024 · Paper 2 · Question 2(a)

The roots of the cubic equation x^3 - 9 = 0 are alpha, beta and gamma.

Determine the cubic equation with roots (alpha - 1), (beta - 1) and (gamma - 1), given that (alpha - 1)(beta - 1) + (alpha - 1)(gamma - 1) + (beta - 1)(gamma - 1) = 12.

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Other parts of this question

  1. 2(b)Calculate the values of p and q.[9 marks]
  2. 2(c)Provide a proof by contradiction for this proposition, by assuming n is odd and showing the assumption is incorrect.[8 marks]

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