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3 marksThe Real Number System – ℝ

CAPE Pure Mathematics Unit 1 · May/June 2011 · Paper 2 · Question 2(a)(ii)

The quadratic equation x² - px + 24 = 0, where p ∈ ℝ, has roots α and β.

Given that α² + β² = 33, find the possible values of p.

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Other parts of this question

  1. 2(a)(i)a)Express α + β in terms of p[1 mark]
  2. 2(a)(i)b)Express α² + β² in terms of p[4 marks]
  3. 2(b)(i)Find the value of f(3)[4 marks]
  4. 2(b)(ii)Find the value of f(9)[2 marks]
  5. 2(b)(iii)Find the value of f(-3).[3 marks]
  6. 2(c)Prove that the product of any two consecutive integers k and k + 1 is an even integer.[2 marks]
  7. 2(d)Prove, by mathematical induction, that n(n² + 5) is divisible by 6 for all positive integers n.[6 marks]

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