Mister exam

# 3x²-27=0 equation

A equation with variable:

#### Numerical solution:

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### The solution

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   2
3*x  - 27 = 0
$$3 x^{2} - 27 = 0$$
Detail solution
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 3$$
$$b = 0$$
$$c = -27$$
, then
D = b^2 - 4 * a * c =

(0)^2 - 4 * (3) * (-27) = 324

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
$$x_{1} = 3$$
$$x_{2} = -3$$
The graph
Sum and product of roots [src]
sum
-3 + 3
$$-3 + 3$$
=
0
$$0$$
product
-3*3
$$- 9$$
=
-9
$$-9$$
-9
Rapid solution [src]
x1 = -3
$$x_{1} = -3$$
x2 = 3
$$x_{2} = 3$$
x2 = 3
Vieta's Theorem
rewrite the equation
$$3 x^{2} - 27 = 0$$
of
$$a x^{2} + b x + c = 0$$
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 9 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -9$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -9$$
x1 = -3.0
x2 = 3.0
x2 = 3.0