[tex]x^4+3x^2+2 = 0\\ \\ \text{Observam ca }i\text{ este solutie.} \\ \\ \Rightarrow x_1 = i,\quad x_2 = -i. \\ \\ x_1+x_2+x_3+x_4 =0 \Rightarrow i-i+x_3+x_4 = 0 \Rightarrow \\ \Rightarrow x_3+x_4 = 0\\\\ x_1x_2x_3x_4 = 2 \Rightarrow i\cdot(-i)\cdot x_3x_4=2 \Rightarrow x_3x_4 = 2\\ \\ t^2-(x_3+x_4)t+x_3x_4 = 0 \\ t^2+2 = 0 \\ \Rightarrow t^2 = -2 \Rightarrow x_{3,4} = \pm i\sqrt{2}[/tex]
[tex]\Rightarrow x^4+3x^2+2 = (x-i)(x+i)(x-i\sqrt 2)(x+i\sqrt 2)[/tex]
