$a=-6.75, b=5, x=-4, x=1-0.5 i$

[Maximum marks: 5 marks]
Note to students: You can and should be using GC here.
$$
\begin{array}{l}
(1+0.5 i)^3+2(1+0.5 i)^2+a(1+0.5 i)+b=0 \\
1.75+3.375 i+a+0.5 a i+b=0
\end{array}
$$
By comparing coefficients of real and imaginary parts,
$$
\begin{array}{l}
a=-\frac{3.375}{0.5}=-6.75 \\
b=-1.75+6.75=5
\end{array}
$$
Using GC, other roots are $-4$ and $1-0.5 i$.