By the complex conjugate root theorem, the one other solution is [tex]1+2i[/tex]
[tex](x-(1-2i))(x-(1+2i))=\\
(x-1+2i)(x-1-2i)=\\
(x-1)^2-(2i)^2=\\
x^2-2x+1+4=\\
x^2-2x+5[/tex]
[tex]\dfrac{x^4-2x^3+6x^2-2x+5}{x^2-2x+5}=x^2+1[/tex]
[tex]x^2+1=0\\
x^2=-1\\
x=i \vee x=-i[/tex]
So, the other solutions are [tex]1+2i,-i,i[/tex]
