(1)What is the root finding technique?
=> In mathematics and computing, a root-finding algorithm is an algorithm for finding zeroes, also called "roots", of continuous functions.As, generally, the zeroes of a function cannot be computed exactly nor expressed in closed form, root-finding algorithms provide approximations to zeroes, expressed either as floating point numbers or as small isolating intervals.
=> Solving an equation f(x) = g(x) is the same as finding the roots of the function h(x) = f(x) – g(x). Thus root-finding algorithms allow solving any equation defined by continuous functions.
(2)Three different techniques for finding the root:
A)Bisection_Method:
=>In mathematics, the bisection method is a root-finding method that applies to any continuous functions for which one knows two values with opposite signs. The method consists of repeatedly bisecting the interval defined by these values and then selecting the subinterval in which the function changes sign, and therefore must contain a root.
B)Newton_raphson
=> the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a single-variable function f defined for a real variable x, the function's derivative f′, and an initial guess x0 for a root of f.
C)False_position:
=>The false position method is a very old method for solving an equation in one unknown. In simple terms, the method is the trial and error technique of using test ("false") values for the variable and then adjusting the test value according to the outcome. This is sometimes also referred to as "guess and check".