A monic quadratic polynomial has the form p(x) = x2+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 $r= -b 2 ± b2- 4c 2 .$ 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 $Cp= 0 -c 1 -b .$ 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 $C\left(p\right).$