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7 marksRoots of Equations

CAPE Pure Mathematics Unit 2 · May/June 2013 · Paper 2 · Question 4(c)(ii)

Complete the table to obtain an approximation of the root of the equation x^3 = 25 correct to 2 decimal places.

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Other parts of this question

  1. 4(a)(i)Obtain the binomial expansion of \sqrt[4]{(1+x)} + \sqrt[4]{(1-x)} up to the term containing x^2.[4 marks]
  2. 4(a)(ii)Hence, by letting x = \frac{1}{16}, compute an approximation of \sqrt[4]{17} + \sqrt[4]{15} to four decimal places.[4 marks]
  3. 4(b)Show that the coefficient of the x^5 term of the product (x+2)^5(x-2)^4 is 96.[7 marks]
  4. 4(c)(i)Use the Intermediate Value Theorem to prove that x^3 = 25 has at least one root in the interval [2, 3].[3 marks]

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