Expand the expression in the equation
$$\frac{\left(- 4 a^{7}\right)^{2}}{a^{12}} = 0$$
We get the quadratic equation
$$16 a^{2} = 0$$
This equation is of the form
a*a^2 + b*a + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$a_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$a_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 16$$
$$b = 0$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (16) * (0) = 0
Because D = 0, then the equation has one root.
a = -b/2a = -0/2/(16)
$$a_{1} = 0$$