# Use the inverse function theorem to estimate the change in the roots

1. Mar 15, 2013

### ianchenmu

1. The problem statement, all variables and given/known data
Let $p(\lambda )=\lambda^3+a_2\lambda^2+a_1\lambda+a_0=(\lambda-x_1)(\lambda-x_2)(\lambda-x_3)$ be a cubic polynomial in 1 variable $\lambda$. Use the inverse function theorem to estimate the change in the roots $0<x_1<x_2<x_3$ if $a=(a_2,a_1,a_0)=(-6,11,-6)$ and $a$ changes by $\Delta a=0.01a$.

2. Relevant equations

n/a

3. The attempt at a solution
How can I use the inverse function theorem to estimate?