I3.1 Given that $\frac{1-\sqrt{3}}{2}$ satisfies the equation $x^{2}+p x+q=0$, where $p$ and $q$ are rational numbers. If $A=|p|+2|q|$, find the value of $A$.
For an equation with rational coefficients, conjugate roots occur in pairs. That is, the other root is $\frac{1+\sqrt{3}}{2}$.
$$
\begin{array}{l}
\frac{1-\sqrt{3}}{2}+\frac{1+\sqrt{3}}{2}=-p \Rightarrow p=-1 \\
\frac{1-\sqrt{3}}{2} \times \frac{1+\sqrt{3}}{2}=q \Rightarrow q=-\frac{1}{2} \\
A=|-1|+2\left|-\frac{1}{2}\right|=2
\end{array}
$$