Newton's Raphson Method

         The  Newton Raphson Method  is referred to as one of the most commonly used techniques for finding the roots of given equations. It can be efficiently generalised to find solutions to a system of equations. Moreover, we can show that when we approach the root, the method is quadratically convergent. In this article, you will learn how to use the Newton Raphson method to find the roots or solutions of a given equation, and the geometric interpretation of this method . Newton Raphson Method Formula Let x 0  be the approximate root of f(x) = 0 and let x 1  = x 0  + h be the correct root. Then f(x 1 ) = 0 ⇒ f(x 0  + h) = 0 ….(1) By expanding the above equation using  Taylor’s theorem , we get: f(x 0 ) + hf 1 (x 0 ) + … = 0 ⇒ h = -f(x 0 ) /f’(x 0 ) Therefore, x 1  = x 0  – f(x 0 )/ f’(x 0 ) Now, x 1  is the better approximation than x 0 . Similarly, the successive approximations x 2 , x 3 , …., x n+1  ar...