Giải phương trình: 2x⁴ – x³ – 5x² + x + 2 = 0.

2x⁴ – x³ – 5x² + x + 2 = 0 (*)

⇔ (2x⁴ + x³ – 2x²) – (2x³ + x² – 2x) – (2x² + x – 2) = 0

⇔ x² (2x² + x – 2) – x (2x² + x – 2) – (2x² + x – 2) = 0

⇔ (2x² + x – 2)(x² – x – 1) = 0

⇔$\left[\begin{array}{l}2x^2+x–2=0\\ x^2–x–1=0\end{array}\right.$

⇔$\left[\begin{array}{l}x=\frac{1\pm \sqrt{5}}{2}\\ x=\frac{-1\pm \sqrt{17}}{4}\end{array}\right.$.