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5 marksAlgebraic Operations

CAPE Pure Mathematics Unit 1 · May/June 1999 · Paper 2 · Question 3(b)(i)

The function f is defined on the set R of real numbers by f: x → (k + 3)x² + kx + 1, where k ∈ R.

Calculate the range of values of k for which the equation f(x) = 0 has no real roots.

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Other parts of this question

  1. 3(a)(i)Find the equation of the line which passes through the point (4, -1) and is perpendicular to the straight line y = -2x + 2.[3 marks]
  2. 3(a)(ii)Calculate the coordinates of the point of intersection of these two straight lines.[3 marks]
  3. 3(b)(ii)Solve the equation f(x) = 0 for k = 1, giving your answer in the form a ± bi, where a, b ∈ R.[3 marks]
  4. 3(b)(iii)Let α and β be roots of f(x) = 0 when k = 8. Without first solving f(x) = 0, determine the equation whose roots are respectively 1/α and 1/β.[6 marks]

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