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а^-12×(-4а^7)^2 equation

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Numerical solution:

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The solution

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       2    
/    7\     
\-4*a /     
-------- = 0
   12       
  a         
$$\frac{\left(- 4 a^{7}\right)^{2}}{a^{12}} = 0$$
Detail solution
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)

$$a_{1} = 0$$
Vieta's Theorem
rewrite the equation
$$\frac{\left(- 4 a^{7}\right)^{2}}{a^{12}} = 0$$
of
$$a^{3} + a b + c = 0$$
as reduced quadratic equation
$$a^{2} + b + \frac{c}{a} = 0$$
$$a^{2} = 0$$
$$a^{2} + a p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$a_{1} + a_{2} = - p$$
$$a_{1} a_{2} = q$$
$$a_{1} + a_{2} = 0$$
$$a_{1} a_{2} = 0$$
The graph
Sum and product of roots [src]
sum
0
$$0$$
=
0
$$0$$
product
0
$$0$$
=
0
$$0$$
0
Rapid solution [src]
a1 = 0
$$a_{1} = 0$$
a1 = 0
Numerical answer [src]
a1 = 0.0
a1 = 0.0