Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x-4)/(x-6)=2
-
Equation e^x=2
-
Equation e^x-x=0
-
Equation 5x-2=1
- Express {x} in terms of y where:
- -2*x+13*y=-6
- -15*x+1*y=10
- -3*x+2*y=0
- -2*x-9*y=1
- Graphing y =:
- x^2
- Derivative of:
-
x^2
- Integral of d{x}:
-
x^2
- Limit of the function:
-
-12
- -12
-
Identical expressions
- x^ two =- twelve
- x squared equally minus 12
- x to the power of two equally minus twelve
- x2=-12
- x²=-12
- x to the power of 2=-12
-
Similar expressions
- x^2=+12
- x^2-9*x+14=0
- (x-1)^2+2(y-2)^2=1
x^2=-12 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x^{2} = -12$$
to
$$x^{2} + 12 = 0$$
This equation is of the form
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
$$a = 1$$
$$b = 0$$
$$c = 12$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = 2 \sqrt{3} i$$
$$x_{2} = - 2 \sqrt{3} i$$
left part with negative sign.
The equation is transformed from
$$x^{2} = -12$$
to
$$x^{2} + 12 = 0$$
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:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 0$$
$$c = 12$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (12) = -48
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2 \sqrt{3} i$$
$$x_{2} = - 2 \sqrt{3} i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 12$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 12$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 12$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 12$$
Sum and product of roots
[src]
sum
___ ___ - 2*I*\/ 3 + 2*I*\/ 3
$$- 2 \sqrt{3} i + 2 \sqrt{3} i$$
=
0
$$0$$
product
___ ___ -2*I*\/ 3 *2*I*\/ 3
$$- 2 \sqrt{3} i 2 \sqrt{3} i$$
=
12
$$12$$
12
Rapid solution
[src]
___ x1 = -2*I*\/ 3
$$x_{1} = - 2 \sqrt{3} i$$
___ x2 = 2*I*\/ 3
$$x_{2} = 2 \sqrt{3} i$$
x2 = 2*sqrt(3)*i
The graph