Min and max eigenvalues of a quadratic form

Question

I have the following quadratic form : $q(x,y,z)=x(y+4z)+y(x-2z)+x^2$, represented by the symmetric matrix $\begin{bmatrix}1&1&2\\1&0&-1\\2&-1&0\end{bmatrix}$. I am asked to find its signature, which appears to be $(2,1)$. And then, I am asked to prove that all of its matrix's eigenvalues are in $]-3,3[$ without computing them. I can't see how to do this.