Mister exam

# 5*x^2-12*x=0 equation

A equation with variable:

#### Numerical solution:

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### The solution

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5*x  - 12*x = 0
$$5 x^{2} - 12 x = 0$$
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
$$a = 5$$
$$b = -12$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =

(-12)^2 - 4 * (5) * (0) = 144

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

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

or
$$x_{1} = \frac{12}{5}$$
$$x_{2} = 0$$
The graph
Sum and product of roots [src]
sum
12/5
$$\frac{12}{5}$$
=
12/5
$$\frac{12}{5}$$
product
0*12
----
5  
$$\frac{0 \cdot 12}{5}$$
=
0
$$0$$
0
Rapid solution [src]
x1 = 0
$$x_{1} = 0$$
x2 = 12/5
$$x_{2} = \frac{12}{5}$$
x2 = 12/5
Vieta's Theorem
rewrite the equation
$$5 x^{2} - 12 x = 0$$
of
$$a x^{2} + b x + c = 0$$
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{12 x}{5} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{12}{5}$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{12}{5}$$
$$x_{1} x_{2} = 0$$
x1 = 2.4
x2 = 0.0
x2 = 0.0