The factorisation of f(x) is
[tex]f(x)=(x+1)(x-2)^2(x^2+x+2)[/tex]
The rational roots are x = -1 and x = 2.
The complex roots are
[tex]x=-\frac{1}{2}+\frac{\sqrt[]{7}}{2}i\text{ and }x=-\frac{1}{2}-\frac{\sqrt[]{7}}{2}i[/tex]
The graph of the function is given below:
