A monic quadratic polynomial has the form
p(x) = x^{2}+bx+c. That was
in HTML. In MathML that equation looks like
$p\left(x\right)={x}^{2}+bx+c.$
The roots
of this polynomial have the form
$$r=\frac{-b}{2}\pm \frac{\sqrt{{b}^{2}-4c}}{2}.$$
If we suppose that $b$
and $c$ are in ℝ, then
the roots are both real, or are complex conjugates.
In any case, the sum of the roots is
$\sum _{i=1}^{2}{r}_{i}.$
Now, every polynomial has a so-called
companion matrix associated with it.
In this case, one form of the companion
matrix is
$$C\left(p\right)=\left[\begin{array}{cc}0& -c\\ 1& -b\end{array}\right].$$
The reason this is called the companion matrix
is that
$\text{det}\left(xI-C\left(p\right)\right)=p\left(x\right).$
It follows that the roots of
$p\left(x\right)$
are exactly the eigenvalues of
$C\left(p\right).$

Here is some SVG that has nothing to do with
companion matrices.