3. If the quadratic equation with real coefficients $a x^{2}+b x+c=0$ has two imaginary roots $x_{1} 、 x_{2}$, and $x_{1}^{3} \in \mathbf{R}$, then $\frac{a c}{b^{2}}=$ $\qquad$ .
3. 1 .

Notice, $x_{2}=\overline{x_{1}}$.
$$
\begin{array}{l}
\text { By } x_{1}^{3} \in \mathbf{R} \Rightarrow x_{1}^{3}=\overline{x_{1}^{3}}=\left(\overline{x_{1}}\right)^{3}=x_{2}^{3} \\
\Rightarrow\left(x_{1}-x_{2}\right)\left(x_{1}^{2}+x_{1} x_{2}+x_{2}^{2}\right)=0 \\
\Rightarrow x_{1}^{2}+x_{1} x_{2}+x_{2}^{2}=0 \\
\Rightarrow\left(x_{1}+x_{2}\right)^{2}=x_{1} x_{2} \\
\Rightarrow\left(-\frac{b}{a}\right)^{2}=\frac{c}{a} \Rightarrow b^{2}=a c \\
\Rightarrow \frac{a c}{b^{2}}=1 .
\end{array}
$$