Quelpr
3 marksRoots of Equations

CAPE Pure Mathematics Unit 2 · May/June 2022 · Paper 2 · Question 4(b)(i)

Use the Intermediate Value Theorem to prove that 4eˣ + 2x² - 5 = 0 has a root in the interval [0, 1].

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 4(a)(i)Show that the binomial expansion of (1 + 5x)^(1/3) up to and including the term in x³ is 1 + x - 2x² + 6x³.[6 marks]
  2. 4(a)(ii)Hence, by letting x = -1/32, compute an estimate of ³√27.[5 marks]
  3. 4(b)(ii)Use four iterations of the interval bisection method to calculate an approximation of the root of 4eˣ + 2x² - 5 = 0 in the interval [0, 1].[6 marks]
  4. 4(b)(iii)Use three iterations of the linear interpolation method to approximate the root of 4eˣ + 2x² - 5 = 0 in the interval (-2, -1).[5 marks]

More practice: the rest of this paper · more Roots of Equations questions · all CAPE Pure Mathematics Unit 2 past papers