\(x^4+x^3+3x^2+2x+2=0\)
\(\Leftrightarrow x^4-x^3+x^2+2x^2-2x+2\)
\(\Leftrightarrow x^2\left(x^2-x+1\right)+2\left(x^2-x+1\right)\)
\(\Leftrightarrow\left(x^2+2\right)\left(x^2-x+1\right)\)
\(\Leftrightarrow\left(x^2+2\right)\left(x^2-x+\frac{1}{4}+\frac{3}{4}\right)\)
\(\Leftrightarrow\left(x^2+2\right)\left[x-\frac{1}{2}^2\right]+\frac{3}{4}\)
Ta co: \(\left(x-\frac{1}{2}\right)^2+\frac{3}{4}>\frac{3}{4}\)
\(\left(x^2+2\right)\left[\left(x-\frac{1}{2}^2\right)+\frac{3}{4}\right]\ge\frac{3}{2}\le0\)