Answer:
x₁=1; x₂=-1; x₃=-0.5; x₄=-2.
Step-by-step explanation:
[tex]2x^4+5x^3-5x-2=0; \ < = > \ 2(x^4-1)+5x(x^2-1)=0; \ < = > \ 2(x^2+1)(x^2-1)+5x(x^2-1)=0; \ < = >[/tex]
[tex](x^2-1)(2x^2+2+5x)=0; \ < = > \ (x^2-1)(2x^2+5x+2)=0; \ = >[/tex]
[tex]= > \ \left[\begin{array}{ccc}x=1\\x=-1\\x=-\frac{1}{2} \\x=-2\end{array}[/tex]
