Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation (a-2)(b+5)=(a-2)b+(a-2)5
-
Equation x+5=0
-
Equation 4*x^2-25=0
-
Equation 8x-15=-12+5x
- Express {x} in terms of y where:
- -14*x+16*y=6
- -4*x-15*y=6
- 8*x-6*y=-18
- -5*x-14*y=18
- Graphing y =:
- 2x+x^3
-
Identical expressions
- 2x+x^ three = zero
- 2x plus x cubed equally 0
- 2x plus x to the power of three equally zero
- 2x+x3=0
- 2x+x³=0
- 2x+x to the power of 3=0
- 2x+x^3=O
-
Similar expressions
- 2x-x^3=0
2x+x^3=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$x^{3} + 2 x = 0$$
transform
Take common factor x from the equation
we get:
$$x \left(x^{2} + 2\right) = 0$$
then:
$$x_{1} = 0$$
and also
we get the equation
$$x^{2} + 2 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{2} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{3} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 0$$
$$c = 2$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{2} = \sqrt{2} i$$
$$x_{3} = - \sqrt{2} i$$
The final answer for 2*x + x^3 = 0:
$$x_{1} = 0$$
$$x_{2} = \sqrt{2} i$$
$$x_{3} = - \sqrt{2} i$$
$$x^{3} + 2 x = 0$$
transform
Take common factor x from the equation
we get:
$$x \left(x^{2} + 2\right) = 0$$
then:
$$x_{1} = 0$$
and also
we get the equation
$$x^{2} + 2 = 0$$
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:
$$x_{2} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{3} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 0$$
$$c = 2$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (2) = -8
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x2 = (-b + sqrt(D)) / (2*a)
x3 = (-b - sqrt(D)) / (2*a)
or
$$x_{2} = \sqrt{2} i$$
$$x_{3} = - \sqrt{2} i$$
The final answer for 2*x + x^3 = 0:
$$x_{1} = 0$$
$$x_{2} = \sqrt{2} i$$
$$x_{3} = - \sqrt{2} i$$
Vieta's Theorem
it is reduced cubic equation
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 2$$
$$v = \frac{d}{a}$$
$$v = 0$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 2$$
$$x_{1} x_{2} x_{3} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 2$$
$$v = \frac{d}{a}$$
$$v = 0$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 2$$
$$x_{1} x_{2} x_{3} = 0$$
Sum and product of roots
[src]
sum
___ ___ - I*\/ 2 + I*\/ 2
$$- \sqrt{2} i + \sqrt{2} i$$
=
0
$$0$$
product
/ ___\ ___ 0*\-I*\/ 2 /*I*\/ 2
$$\sqrt{2} i 0 \left(- \sqrt{2} i\right)$$
=
0
$$0$$
0
Rapid solution
[src]
x1 = 0
$$x_{1} = 0$$
___ x2 = -I*\/ 2
$$x_{2} = - \sqrt{2} i$$
___ x3 = I*\/ 2
$$x_{3} = \sqrt{2} i$$
x3 = sqrt(2)*i