Find a root of the following function using hand calculations $($Not a MATLAB function or script$)$

by

ax$\_(0)=-3,$ and

bx$\_(0)=5\mathrm{.}1.$

cf$($x$)=$x$^(5)-11\mathrm{.}9$x$^(4)+43\mathrm{.}78$x$^(3)-41\mathrm{.}3$x$^(2)-44\mathrm{.}78$x$+53\mathrm{.}2$

For each method, perform the computations until $\backslash$epsi $\_($a$)$ is less than $1\%.$ Also check your final answer.

Most of the work should be done by hand calculations $($you can use MATLAB only as a

calculator for this problem$).$