X^5+2x^4-3x^3-3x^2+x+1=0

Question

X^5+2x^4-3x^3-3x^2+x+1=0

Answer 1

x^4 (x+1) - 3x^2 (x+1) + (x+1)=0

(x+1)(x^4 - 3x^2+1)=0

x+1=0 --> x= -1

x^4 - 3x^2+1=0 --> D=9-4=5 -->

x^2=(3+sqrt5)/2 --> x=sqrt((3+sqrt5)/2), x= -sqrt((3+sqrt5)/2)

 x^2=(3-sqrt5)/2 --> x=sqrt((3-sqrt5)/2), x= -sqrt((3-sqrt5)/2)