Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The graph is defined by the equation $y = f(x)$, where $f(x) = x^4 - 5x^3 + 6x^2 + 5x - 15$. The diagram shows that the curve intersects the $x$-axis at $A$ and $B$, whose coordinates are $(a, 0)$ and $(b, 0)$ respectively.
(a)[2]
Use the factor theorem to demonstrate that $(x - 3)$ is a factor of $f(x)$.
(b)[5]
After first determining the quotient obtained when $f(x)$ is divided by $(x - 3)$, show that $a = -\sqrt{\frac{5}{2 - a}}$.
(c)[3]
Use an iterative method, based on the equation in part (b), to determine the value of $a$ correct to 3 significant figures. Show the outcome of each iteration to 5 significant figures.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Replace $x=3$ and try to evaluate” …