Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The equation $x^3 - x^2 - 6 = 0$ has a single real root, written as $\alpha$.
(i)[2]
Find, by calculation, the pair of consecutive integers that enclose $\alpha$.
(ii)[2]
Show that, should a sequence generated by the iterative formula $x_{n+1} = \sqrt{x_n + \frac{6}{x_n}}$ converge, its limit is $\alpha$.
(iii)[3]
Use this iterative formula to determine $\alpha$ correct to $3$ decimal places. Record each iterate to $5$ decimal places.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Evaluate, or examine the sign of, $x^3-x^2-6$ at two integer values of $x$, or an equivalent method” …