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8 marksThe Real Number System – ℝ

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

This question involves properties of quadratic and cubic equations, and functions involving absolute values.

Determine the values of the real number h for which the roots of the quadratic equation 4x² - 2hx + (8 – h) = 0 are real.

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Other parts of this question

  1. 1(a)(ii)The roots of the cubic equation x³ - 15x² + px – 105 = 0 are 5 - k, 5 and 5 + k. Find the values of the constants p and k.[7 marks]
  2. 1(b)(i)Copy the table below and complete by inserting the values for the functions f(x) = |x + 2 | and g(x) = 2 |x − 1 |.[4 marks]
  3. 1(b)(ii)Using a scale of 1 cm to 1 unit on both axes, draw on the same graph f(x) and g(x) for −3 ≤ x ≤ 5.[4 marks]
  4. 1(b)(iii)Using the graphs, find the values of x for which f(x) = g(x).[2 marks]

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