Evaluate: x^2+6x+12

Expression: ${x}^{2}+6x+12$

To find the roots of the polynomial, set the expression equal to $0$

${x}^{2}+6x+12=0$

Solve using the quadratic formula

$\begin{array} { l }x=-3+\sqrt{ 3 }i,\\x=-3-\sqrt{ 3 }i\end{array}$

The roots of the polynomial are the solutions of the corresponding polynomial equation

$\begin{align*}&\begin{array} { l }-3+\sqrt{ 3 }i,& -3-\sqrt{ 3 }i\end{array} \\&\begin{array} { l }\approx-3+1.7321i,& \approx-3-1.7321i\end{array}\end{align*}$