A-level · Numerical methods

Locating roots by change of signExam-style questions

Trapping a root of f(x) = 0 in an interval using the change-of-sign rule — why continuity is essential, what a sign change does and doesn't guarantee, and refining a root to a given number of decimal places.

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22 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
Show that the equation $x^3 - 2x - 5 = 0$ has a root between $x = 2$ and $x = 3$ .
Level 2 · 2 marksTry it
2
Show that $x^3 - 7x + 2 = 0$ has a root between $x = 0$ and $x = 1$ .
Level 2 · 2 marksTry it
3
Show that the equation $x^{3} + 2x - 7 = 0$ has a root between $x = 1$ and $x = 2$ . (2 marks)
Level 2 · 2 marksTry it
4
The diagram shows part of the curve $y = \text{g}(x)$ . The function $\text{g}$ is a polynomial of degree $4$ , and the curve meets the $x$ -axis at exactly three points.State which root of the equation $\text{g}(x) = 0$ cannot be located by a change of sign method, giving a reason for your answer.

(2 marks)
Level 2 · 2 marksTry it