Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram displays the curve $y = x^4 - 2x^3 - 7x - 6$. The curve meets the $x$-axis at the points $(a, 0)$ and $(b, 0)$, where $a < b$. It is stated that $b$ is an integer.
(i)[1]
Determine the value of $b$.
(ii)[4]
Hence prove that $a$ satisfies the equation $a = -\frac{1}{3}(2 + a^2 + a^3)$.
(iii)[3]
Apply an iterative formula based on the equation in part (ii) to find $a$ correct to 3 decimal places. Record every iteration to 5 decimal places.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State that $b = 3$” …