GATE IT 2008 | Question: 30

Question

Consider the function f(x) = x² - 2x - 1. Suppose an execution of the Newton-Raphson method to find a zero of f(x) starts with an approximation x₀ = 2 of x. What is the value of x₂, the approximation of x that algorithm produces after two iterations, rounded to three decimal places?

• A. 2.417
• B. 2.419
• C. 2.423
• D. 2.425

Answer 1

In newton method, if current guess is x_cur, then new guess x_new is

x_new = x_cur - f(x_cur)/f'(x_cur)

Now Initially, x_cur = 2, so after 1^st iteration,

x_new = 2 - (-1)/2 = 2.5

Now x_cur becomes 2.5, so after 2^nd iteration,

x_new = 2.5 - (0.25)/3 = 2.417