4
\end{array} \right) , \quad \mathbf { D } = \left( \begin{array} { l l l }
2 & - 1 & 5
\end{array} \right)$$
and
$$\mathbf { E } = \mathbf { C D }$$
find \(\mathbf { E }\).
3.
$$f ( x ) = \frac { 1 } { 2 } x ^ { 4 } - x ^ { 3 } + x - 3$$
- Show that the equation \(\mathrm { f } ( x ) = 0\) has a root \(\alpha\) between \(x = 2\) and \(x = 2.5\)
[0pt] - Starting with the interval [2,2.5] use interval bisection twice to find an interval of width 0.125 which contains \(\alpha\).
The equation \(\mathrm { f } ( x ) = 0\) has a root \(\beta\) in the interval \([ - 2 , - 1 ]\).
- Taking - 1.5 as a first approximation to \(\beta\), apply the Newton-Raphson process once to \(\mathrm { f } ( x )\) to obtain a second approximation to \(\beta\). Give your answer to 2 decimal places.
4.
$$f ( x ) = \left( 4 x ^ { 2 } + 9 \right) \left( x ^ { 2 } - 2 x + 5 \right)$$ - Find the four roots of \(\mathrm { f } ( x ) = 0\)
- Show the four roots of \(\mathrm { f } ( x ) = 0\) on a single Argand diagram.