This is what I've atempted so far in solving $\lambda^3 - 3.250\lambda^2 + \lambda - 0.063 = 0$. The following are the steps:
step 1: $f(\lambda) = \lambda^3 - 3.250\lambda^2 + \lambda - 0.063 $
step 2a: $f(0) = -0.063$
step 2b: $f(1) = -1.313$
step 3: $f(2) = -4.063$
step 4: $f(3) = -17.313$
step 5: $f(4) = 14.937$
This shows that the value of the root is close to $\lambda = 3$. Now we use the iterative formula: $r_{4} = r_{3} - \frac{f(r_{3})}{f^\prime(r_{3})}$
where $f(r_{3}) = -17.313$ and $f^\prime(r_{3}) = 8.5$. Then we compute $r_{4} = 3-\frac{(-17.313)}{8.5} = 5.0368$
Question: Have I followed the preliminary steps correctly?