I trying to find smallest (not by absolute value) root in equation: $\det{(B + Ax + Ix^2)} = 0$, where $x \in \mathbb{R}$ and matrices $A$ and $B$ are symmetric.
I would like to find a solution in one of two ways:
Perhaps there are methods to find all the roots purely mathematically, I would be glad to hear where I could read about this.
I think that you can find the root by iterative methods, but I don’t know of one that would help find the smallest one.
Can anyone help me with such question?