Given the equation:
[tex]3x^2+ax+b=0[/tex]Divide the equation by 3, to make the coefficient of x = 1
so,
[tex]x^2+\frac{a}{3}x+\frac{b}{3}=0[/tex]Given: 1 - 2i is a root of the equation
Note: the root is a complex number, while (b/3) is a real number
So, the other toot will be conjugate to the given root
so,
[tex]\begin{gathered} \frac{b}{3}=(1-2i)\cdot(1+2i)=1-4i^2=1-4\cdot(-1)=1+4=5 \\ b=5\cdot3=15 \end{gathered}[/tex]so, the value of b = 15
