Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram depicts the curve $y=x^4+2x^3+2x^2-4x-16$, which meets the $x$-axis at the points $(\alpha,0)$ and $(\beta,0)$ with $\alpha<\beta$. It is stated that $\alpha$ is an integer.
(i)[2]
Find the value of $\alpha$.
(ii)[3]
Show that $\beta$ satisfies $x=\sqrt[3]{8-2x}$.
(iii)[3]
Apply the iteration process based on the equation in part (ii) to determine the value of $\beta$ correct to 2 decimal places. Show the outcome of each 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: “Find the value of $y$ when $x=-2$” …