1. Given the real number $y=\log _{2}\left[a x^{2}+(a-1) x+\frac{1}{4}\right]$ has a domain of all real numbers, the range of real number $a$ is ( ).
A. $\left(0, \frac{3+\sqrt{5}}{2}\right)$
B. $\left(\frac{3-\sqrt{5}}{2}, 1\right)$
C. $\left(-\infty, \frac{3-\sqrt{5}}{2}\right) \cup\left(\frac{3+\sqrt{5}}{2},+\infty\right)$
D. $\left(\frac{3-\sqrt{5}}{2}, \frac{3+\sqrt{5}}{2}\right)$
1. A. $a x^{2}+(a-1) x+\frac{1}{4}>0$ holds for all real numbers $x$, then $\left\{\begin{array}{l}a>0 \\ \Delta<0,\end{array}\right.$ which gives $0<a<\frac{3+\sqrt{5}}{2}$.