Okay, here we have this:
Considering the provided equation, we are going to find all the roots, so we obtain the following:
[tex]\begin{gathered} x^4-2x^3+x^2-8x-12=0 \\ \mleft(x+1\mright)\mleft(x-3\mright)\mleft(x^2+4\mright)=0 \\ x+1=0\quad \mathrm{or}\quad \: x-3=0\quad \mathrm{or}\quad \: x^2+4=0 \\ x=-1\quad \mathrm{or}\quad \: x=3\quad \mathrm{or}\quad \: x^2=-4 \\ x=-1\quad \mathrm{or}\quad \: x=3\quad \mathrm{or}\quad \: x=\sqrt[]{-4} \\ x=-1,\: x=3,\: x=2i,\: x=-2i \end{gathered}[/tex]
Finally we obtain that the correct answer is the second option.
