4x^4+2x^3-8x^2+x+1=0
4x^4+2x^3-6x^2-2x^2+x+1=0
x^2(4x^2+2x-6)-2x^2+x+1=0
2x^2(2x^2+x-3)-2x^2+x+1=0
2x^2(2(x-1)(x+3/2))-(2x^2-x-1)=0
2x^2(x-1)(2x+3)-(2(x-1)(x+1/2))=0
2x^2(x-1)(2x+3)-(x-1)(2x+1)=0
(2x^2(2x+3)-(2x+1)(x-1)=0
(4x^3+6x^2-2x-1)(x-1)=0
(4x^3+6x^2-4x+2x-1)(x-1)=0
(2x(2x^2+3x-2)+2(x-1/2))(x-1)=0
(2x(2(x-1/2)(x+2))+2(x-1/2))(x-1)=0
(4x(x-1/2)(x+2)+2(x-1/2))(x-1)=0
(x-1)(x-1/2)(4x(x+2)+2)=0
(x-1)(x-1/2)(4x^2+8x+2)=0
x-1=0 или x-1/2=0 или 4x^2+8x+2=0
x=1 или x=1/2 или 4x^2+8x+2=0
4x^2+8x+2=0
2x^2+4x+1=0
D=16-8=8
x=(-4+√8)/4=(-4+2√2)/4=-1+√2/2
x= -1-√2/2
Ответ: 1;1/2;-1+√2/2;-1-√2/2