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7 marksCubic Functions and Equations

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

The roots of the cubic equation x³ + 3px² + qx + r = 0 are 1, -1 and 3.

Find the values of the real constants p, q and r.

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Other parts of this question

  1. 1(b)(i)Without using calculators or tables, show that (√6 + √2) / (√6 - √2) = 2 + √3.[5 marks]
  2. 1(b)(ii)Without using calculators or tables, show that (√6 + √2) / (√6 - √2) + (√6 - √2) / (√6 + √2) = 4.[5 marks]
  3. 1(c)(i)Show that Σ (from r=1 to n) r(r + 1) = (1/3)n(n + 1)(n + 2), n ∈ N.[5 marks]
  4. 1(c)(ii)Hence, or otherwise, evaluate Σ (from r=31 to 50) r(r + 1).[3 marks]

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