`x^6-x^3+x^2-x+1`
`⇔x^6-1/2 . x^3 - 1/2 . x^3 +1/4 + x^2-1/2 . x- 1/2 . x+1/4 +2/4`
`⇔x^3(x^3-1/2)-1/2(x^3-1/2)+x(x-1/2)-1/2(x-1/2) +1/2`
`⇔(x^3-1/2)(x^3-1/2)+(x-1/2)(x-1/2)+1/2`
`⇔(x^3-1/2)^2+(x-1/2)^2+1/2`
Ta có :
`(x^3-1/2)^2 ≥ 0 ∀ x`
`(x-1/2)^2 ≥ 0 ∀ x`
`⇒(x^3-1/2)^2+(x-1/2)^2≥0 ∀ x`
`⇒(x^3-1/2)^2+(x-1/2)^2+1/2 > 0 `
⇒Đa thức vô nghiệm
