Question

The Newton-Raphson method is used to find the root of \[ f(x)=x^2-x-1=0 \] If the initial guess is \(x_0=1\), then the estimate after two iterations is

• A. \(2\)
• B. \(1.80\)
• C. \(1.67\)
• D. \(1.82\)

Hint:

Newton-Raphson converges quickly: \[ \boxed{x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}} \] Always recompute derivative at each step.

Answer 1

The Correct Option is D