Task $2$:

$($a$)$ Use suitable initial approximation$($s$)$ for each of the following iterative method to find one of the

real roots of the equation $2x^2-x+e^{2x}-3=0$ correct to four significant figures.

$($i$)$ Newton$-$Raphson method,

$($ii$)$ Fixed$-$point iteration method,

$($iii$)$ Secant method,

$($iv$)$ Bisection method.