Mathematics 9709 · AS & A Level · Numerical solution of equations

Numerical solution of equations — practice question

Define $f(x)$ by $f(x)=2x^3 - 5x^2 + 4$.
(a)[2]

Show that, should the sequence defined by $x_{n+1} = \sqrt{\frac{4}{5 - 2x_n}}$ converge, its limit is a solution of $f(x) = 0$.

(b)[3]

The equation has a root near $1.2$. Using the iterative formula from part (a) and the starting value $1.2$, find the root correct to $2$ decimal places. Give each iteration to $4$ decimal places.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: State or imply $x=\sqrt{\tfrac{4}{5-2x}}$ before squaring.

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