Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram displays the curve $y = x^4 + 2x - 9$. This curve meets the positive $x$-axis at point $P$.
(i)[2]
Use calculation to confirm that the $x$-coordinate of $P$ is between $1.5$ and $1.6$.
(ii)[1]
Show that the $x$-coordinate of $P$ satisfies the equation $x = \sqrt[3]{\left(\frac{9}{x} - 2\right)}$.
(iii)[3]
Use the iterative formula $x_{n+1} = \sqrt[3]{\left(\frac{9}{x_n} - 2\right)}$ to find the $x$-coordinate of $P$ correct to $2$ decimal places. Give the outcome of each iteration to $4$ decimal places.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Consider whether $x^4 + 2x - 9$ is positive or negative when $x = 1.5$ and when $x = 1.6$.” …