Given:
[tex]x^5-3x^4-8x^3-8x^2-9x-5=0[/tex]
the given polynomial is of degree 5. So, according to the first fundamental theorem of algebra, the given polynomial has 5 roots.
Find the root of the polynomial by synthetic division.
The complex roots are,
[tex]\begin{gathered} x^2+1=0 \\ x^2=-1 \\ x=\sqrt[]{-1} \\ x=\pm i \end{gathered}[/tex]
Answer: complex roots of the polynomial is i and -i.
