`x^4-5x^3+10x+4=0`
`⇔x^4-3x^3-6x^2-2x-2x^3+6x^2+12x+4=0`
`⇔x(x^3-3x^2-6x-2)-2(x^3-3x^2-6x-2)=0`
`⇔(x^3-3x^2-6x-2)(x-2)=0`
`⇔(x^3+x^2-4x^2-4x-2x-2)(x-2)=0`
`⇔[x^2(x+1)-4x(x+1)-2(x+1)](x-2)=0`
`⇔(x+1)(x^2-4x-2)(x-2)=0`
`⇔`\(\left[ \begin{array}{l}x+1=0\\x^2-4x-2=0\\x-2=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=-1\\x^2-4x-2=0\\x=2\end{array} \right.\)
Xét `x^2-4x-2=0`
`Δ'=(-2)^2-(-2)=6>0`
`->` Phương trình có hai nghiệm phân biệt:
`x_1=(-(-2)-\sqrt{6})/1=2-\sqrt{6}`
`x_2=(-(-2)+\sqrt{6})/1=2+\sqrt{6}`
Vậy `S={-1;2;2-\sqrt{6};2+\sqrt{6}}`
