Multiple Intersection points - 2

Given the function: $f(x)=e^{2x}+(1-a x^2)e^x-a x^2 \ (a \in \mathbb R)$ .

If equation: $f(x)=0$ has three distinct roots, find the range of $a$ .

The range can be expressed as $(A,+\infty)$ , submit $\lfloor 10000A \rfloor$ .