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4 marksThe Real Number System – ℝ

CAPE Pure Mathematics Unit 1 · May/June 2008 · Paper 2 · Question 2(a)(iii)

The roots of the quadratic equation 2x² + 4x + 5 = 0 are α and β. Without solving the equation:

Find a quadratic equation whose roots are α³ and β³.

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Other parts of this question

  1. 2(a)(i)Write down the values of α + β and αβ.[2 marks]
  2. 2(a)(ii)a)Calculate α² + β².[2 marks]
  3. 2(a)(ii)b)Calculate α³ + β³.[4 marks]
  4. 2(b)(i)Solve for x the equation x^(1/3) - 4x^(-1/3) = 3.[5 marks]
  5. 2(b)(ii)Find x such that log₂(x + 3) + log₂(x - 1) = 1.[5 marks]
  6. 2(b)(iii)Without the use of calculators or tables, evaluate log₁₀(1/2) + log₁₀(2/3) + log₁₀(3/4) + ... + log₁₀(8/9) + log₁₀(9/10).[3 marks]

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