Ta có:
x^5-x^4+3x^3+3x^2-x+1=0
<=> (x^5 + x^4)-(2x^4+2x^3)+(5x^3+5x^2) -(2x^2+2x)+(x+1)
<=> x^4(x+1)-2x^3(x+1)+
5x^2(x+1) -2x(x+1)+(x+1)=0
<=> (x+1)(x^4-2x^3+5x^2-2x+1)=0
<=> x+1=0 hoặc x^4-2x^3+5x^2-2x+1=0
<=> x=-1
Vì x^4-2x^3+5x^2-2x+1
= x^4-2x^3+x^2+4x^2-2x+1/4+3/4
= x^2(x-1)^2+(2x-1/2)^2+3/4>0 với mọi x
Vậy S={-1}