Year 11 Maths - Methods Polynomials

Bisection Method

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Questions

Question 1

28697

Find an approximation to the root of the function \(f\left( x \right) = {x^3} - x - 2\) for \(\left[ {1,2} \right]\), by the one application of the bisection method.

Answer

\(x = 1.5\)

Worked Solution

\begin{align}
&\begin{aligned}
f(1)&=1-1-2=-2 \\
f(2)&=8-2-2=4
\end{aligned}\\
&\therefore \text{A root is between } x=1 \text{ and } x=2\\
&\begin{aligned}
x&=\frac{1+2}{2}=1.5 \\
f(1.5)&=-0.125
\end{aligned}\\
&\therefore x=1.5 \text{ is a better approximation}
\end{align}

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