3x^2 - 7x + 12 = 0 this doesn't factor......using the onsite solver, we have
$${\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{12}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{95}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{7}}\right)}{{\mathtt{6}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{95}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}}\right)}{{\mathtt{6}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}\left({\mathtt{\,-\,}}{\frac{{\mathtt{7}}}{{\mathtt{6}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1.624\: \!465\: \!724\: \!134}}{i}\right)\\
{\mathtt{x}} = {\frac{{\mathtt{7}}}{{\mathtt{6}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1.624\: \!465\: \!724\: \!134}}{i}\\
\end{array} \right\}$$
The sum of the roots = (14 / 6) =( 7 / 3 )
The product of the roots is
(1/36)[(7 - (√95)i] [ (7 + (√95)i ] =
(1/36) [49 - 95i2] =
(1/36) [ 49 + 95] =
(1/36)[144] = 4
+130511 