Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The polynomial $p(x)$ is given by $p(x) = x^4 - 3x^3 + 3x^2 - 25x + 48$. The diagram depicts the curve $y = p(x)$, which meets the $x$-axis at $(\alpha, 0)$ and $(3, 0)$.
(i)[5]
Divide $p(x)$ by a suitable linear factor and so show that $\alpha$ is a root of the equation $x = \sqrt[3]{16 - 3x}$.
(ii)[3]
Use the iterative formula $x_{n+1} = \sqrt[3]{16 - 3x_n}$ to determine $\alpha$ correct to 2 decimal places. Show the result of every iteration to 4 decimal places.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Take $x-3$ as the divisor” …