One method to determinate the roots is plotting the function and determinate where it crosses with the x axis. This point, represents the x value for which f(x)=0, give us an approximation of the root.
For example: Find the real roots of the function: f(x)=-0.5x + 1.8x + 6.3 with the graphical method.
The bisection method is one type of incremental search method where the interval is always divided in the half. The root is determined as lying at the midpoint of the subinterval within which the sign change occurs. The process is iterative.
“ An alternative method that exploits tis graphical insight is to join f(xi) and f(xu) by a straight line. The intersection of this line with the x axis represents an improved estimate of the root. The fact that the replacement of the curve by a straight line gives a “false position”. Source: CHAPRA, numerical methods for engineers.
The intersection of the line with the x axis can be estimated as Source: Internet
Another option to find this roots is to incorporate an incremental search at the beginning of the computer program. This method consist in taking one end of the region of interest and then evaluate the function at small increments across the region. The point is: When the function changes the sign this mean that in that point there is a root .