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Question 30

Show that the equation $x^3 + 4x = 1$ has a solution between $x = 0$ and $x = 1$ .

[2]

Show that the equation $x^3 + 4x = 1$ can be rearranged to give: $x=14−x34\displaystyle x = \frac{1}{4} - \frac{x^3}{4}$

[1]

Starting with $x_0 = 0$ , use the iteration formula $xn+1=14−xn34\displaystyle x_{n+1} = \frac{1}{4} - \frac{x_n^3}{4}$ twice to find an estimate for the solution to $x^3 + 4x = 1$

[3]

Markscheme

Iteration Questions

GCSE
Maths
Iteration

40 exam-style questions on AQA GCSE Maths Iteration. Each one has a worked solution and a mark scheme showing where the marks go.

Iteration

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Question 30

Show that the equation $x^3 + 4x = 1$ has a solution between $x = 0$ and $x = 1$ .

[2]

Show that the equation $x^3 + 4x = 1$ can be rearranged to give: $x=14−x34\displaystyle x = \frac{1}{4} - \frac{x^3}{4}$

[1]

Starting with $x_0 = 0$ , use the iteration formula $xn+1=14−xn34\displaystyle x_{n+1} = \frac{1}{4} - \frac{x_n^3}{4}$ twice to find an estimate for the solution to $x^3 + 4x = 1$

[3]

Markscheme

Iteration Questions

GCSE
Maths
Iteration

40 exam-style questions on AQA GCSE Maths Iteration. Each one has a worked solution and a mark scheme showing where the marks go.