$($a$)$ Describe the differences between analytic and algorithmic solutions.

$($b$)$ Develop the pseudocode for an algorithmic solution for finding the two

points where the function f$($x$)=3$x$2-12\mathrm{.}4$x $+3$ crosses the x$-$axis.

$($c$)$ Use an analytical solution of the function to determine the two crossing points.