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x^2-2x+4=0

x^2-2x+4=0 equation

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Numerical solution:

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The solution

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 2              
x  - 2*x + 4 = 0
$$\left(x^{2} - 2 x\right) + 4 = 0$$
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
$$a = 1$$
$$b = -2$$
$$c = 4$$
, then
D = b^2 - 4 * a * c = 

(-2)^2 - 4 * (1) * (4) = -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
$$x_{1} = 1 + \sqrt{3} i$$
$$x_{2} = 1 - \sqrt{3} i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = 4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = 4$$
The graph
Sum and product of roots [src]
sum
        ___           ___
1 - I*\/ 3  + 1 + I*\/ 3 
$$\left(1 - \sqrt{3} i\right) + \left(1 + \sqrt{3} i\right)$$
=
2
$$2$$
product
/        ___\ /        ___\
\1 - I*\/ 3 /*\1 + I*\/ 3 /
$$\left(1 - \sqrt{3} i\right) \left(1 + \sqrt{3} i\right)$$
=
4
$$4$$
4
Rapid solution [src]
             ___
x1 = 1 - I*\/ 3 
$$x_{1} = 1 - \sqrt{3} i$$
             ___
x2 = 1 + I*\/ 3 
$$x_{2} = 1 + \sqrt{3} i$$
x2 = 1 + sqrt(3)*i
Numerical answer [src]
x1 = 1.0 - 1.73205080756888*i
x2 = 1.0 + 1.73205080756888*i
x2 = 1.0 + 1.73205080756888*i
The graph
x^2-2x+4=0 equation