In this question, the root$-$finding of a function is considered.

Function:

$f(x)=3x^2-2x-8$

Complete the following:

Provide a plot of $f(x)$ and identify, graphically, the approximate location$($s$)$ of the roots of the function.

Provide analytical solutions for the problem.

Providing screenshots and commentary, carry out an investigation using both the Bisection Method and Newton$-$Raphson Methods.

Consider different tolerances $($i$.$e$.,$ Tol $=0\mathrm{.}1,0\mathrm{.}01$ and $0\mathrm{.}001.$ What are the implications of the variations in these values of tolerance? PLS use Matlab and show the code