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6 marksAlgebraic Operations

CAPE Pure Mathematics Unit 1 · May/June 2007 · Paper 2 · Question 1(b)(ii)

A function f is defined by f(x) = x^4 - 9x^3 + 28x^2 - 36x + 16, where x is a real number; and u = x + 4/x, where x ≠ 0.

By writing f(x) = x^2 [x^2 - 9x + 28 - 36/x + 16/x^2] and using the result from (b)(i) above, show that if f(x) = 0, then u^2 - 9u + 20 = 0.

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Other parts of this question

  1. 1(a)Find all the real factors of g(x).[3 marks]
  2. 1(a)(ii)Find all the real roots of g(x) = 0.[1 mark]
  3. 1(b)(i)Express u^2 in terms of x.[3 marks]
  4. 1(b)(iii)Hence, determine the values of x ∈ R for which f(x) = 0.[7 marks]

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