We know that one root is 1-2i, and as the imaginary roots are conjugates, we obtain that the another root should be 1+2i. This means that we are able to factorize the polynomial as:
[tex](x-(1-2i))(x-(1+2i))=3x^2+ax+b[/tex]And, as such, the value of b will be the multiplication of both roots (because is the coefficient without a letter). In this case,
[tex]\begin{gathered} b=(1-2i)(1+2i) \\ =1-(2i)^2 \\ =1-4i^2 \\ =1-4(-1) \\ =1+4=5 \end{gathered}[/tex]This means that the value of b must be 5.
