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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 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

Because D = 0, then the equation has one root.

$$a_{1} = 0$$

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

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

$$a_{1} + a_{2} = - p$$

$$a_{1} a_{2} = q$$

$$a_{1} + a_{2} = 0$$

$$a_{1} a_{2} = 0$$

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

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

$$a_{1} + a_{2} = - p$$

$$a_{1} a_{2} = q$$

$$a_{1} + a_{2} = 0$$

$$a_{1} a_{2} = 0$$