The purpose of calculating the roots of an equation to determine the values of x for which holds:
f(x) =0
The determination of the roots of an equation is one of the oldest problem and there have been many efforts in this regard. His importance is that if we can determine the roots of an equation. we can also determine the maximum and minimum, own values of a counterfoils, solve system of liner and differential equations.
Some methods used to obtain roots of an equation are:
Bracketing Methods
These techniques are called Bracketing methods because two initial guesses for the root are required.As the name implies , these guesses must bracket or be on either side of the root. The particular methods described herein employ different strategies to systematically reduce the width of the bracket and, hence , home in on correct answer.
-Graphical Method
-The Bisection Method
Open Methods
The open methods described are based on formulas that require only a single starting value of x or two starting values that do not necessarily bracket the root. As such, they sometimes diverge or move away from the root.
-Newton Raphson Method
-The Secant Method
