Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^4-2*x^2-15=0
-
Equation x^2-8x=0
-
Equation x^2-6x-27=0
-
Equation x^2=-3
- Express {x} in terms of y where:
- 8*x+1*y=4
- 20*x-16*y=7
- -3*x+19*y=16
- 8*x-16*y=14
- Graphing y =:
- x^2
- Derivative of:
-
x^2
-
-3
- Integral of d{x}:
-
x^2
-
-3
- Sum of series:
-
-3
-
Identical expressions
- x^ two =- three
- x squared equally minus 3
- x to the power of two equally minus three
- x2=-3
- x²=-3
- x to the power of 2=-3
-
Similar expressions
- a^2*x^2+a*x-21*a+1=0
- x^2+5=0
- 6x^2-35x+50=0
- a*x^2-2a*x+2x+1=0
- x^2-10*y+2x+y^2+26=0
- x^2=+3
x^2=-3 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
$$x^{2} = -3$$
to
$$x^{2} + 3 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = 3$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = \sqrt{3} i$$
$$x_{2} = - \sqrt{3} i$$
left part with negative sign.
The equation is transformed from
$$x^{2} = -3$$
to
$$x^{2} + 3 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = 3$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (3) = -12
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
$$x_{1} = \sqrt{3} i$$
$$x_{2} = - \sqrt{3} i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 3$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 3$$
Rapid solution
[src]
___ x1 = -I*\/ 3
$$x_{1} = - \sqrt{3} i$$
___ x2 = I*\/ 3
$$x_{2} = \sqrt{3} i$$
x2 = sqrt(3)*i
Sum and product of roots
[src]
sum
___ ___ - I*\/ 3 + I*\/ 3
$$- \sqrt{3} i + \sqrt{3} i$$
=
0
$$0$$
product
___ ___ -I*\/ 3 *I*\/ 3
$$- \sqrt{3} i \sqrt{3} i$$
=
3
$$3$$
3
The graph