Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2-6x+5=0
- Equation x^2+y^2=9
- Equation (3x−36)⋅(x+8)=0
-
Equation x^2+12=0
- Express {x} in terms of y where:
- 12*x-3*y=-2
- 5*x+4*y=7
- 14*x+1*y=3
- 16*x+16*y=-4
- Graphing y =:
- x^2+12
- Factor polynomial:
- x^2+12
-
Identical expressions
- x^ two + twelve = zero
- x squared plus 12 equally 0
- x to the power of two plus twelve equally zero
- x2+12=0
- x²+12=0
- x to the power of 2+12=0
- x^2+12=O
-
Similar expressions
- x^2-12=0
x^2+12=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
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
$$x_{1} = 2 \sqrt{3} i$$
$$x_{2} = - 2 \sqrt{3} i$$
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