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2x^2-8x+11 equation

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Numerical solution:

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The solution

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   2               
2*x  - 8*x + 11 = 0
(2x2−8x)+11=0\left(2 x^{2} - 8 x\right) + 11 = 0
Simplify
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:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=2a = 2
b=−8b = -8
c=11c = 11
, then
D = b^2 - 4 * a * c = 

(-8)^2 - 4 * (2) * (11) = -24

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
x1=2+6i2x_{1} = 2 + \frac{\sqrt{6} i}{2}
x2=2−6i2x_{2} = 2 - \frac{\sqrt{6} i}{2}
Vieta's Theorem
rewrite the equation
(2x2−8x)+11=0\left(2 x^{2} - 8 x\right) + 11 = 0
of
ax2+bx+c=0a x^{2} + b x + c = 0
as reduced quadratic equation
x2+bxa+ca=0x^{2} + \frac{b x}{a} + \frac{c}{a} = 0
x2−4x+112=0x^{2} - 4 x + \frac{11}{2} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−4p = -4
q=caq = \frac{c}{a}
q=112q = \frac{11}{2}
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=4x_{1} + x_{2} = 4
x1x2=112x_{1} x_{2} = \frac{11}{2}
The graph
0.01.02.03.04.05.06.07.0020
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
        ___           ___
    I*\/ 6        I*\/ 6 
2 - ------- + 2 + -------
       2             2
(2−6i2)+(2+6i2)\left(2 - \frac{\sqrt{6} i}{2}\right) + \left(2 + \frac{\sqrt{6} i}{2}\right) 
=
4
44 
product
/        ___\ /        ___\
|    I*\/ 6 | |    I*\/ 6 |
|2 - -------|*|2 + -------|
\       2   / \       2   /
(2−6i2)(2+6i2)\left(2 - \frac{\sqrt{6} i}{2}\right) \left(2 + \frac{\sqrt{6} i}{2}\right) 
=
11/2
112\frac{11}{2} 
11/2
Rapid solution [src] 
             ___
         I*\/ 6 
x1 = 2 - -------
            2
x1=2−6i2x_{1} = 2 - \frac{\sqrt{6} i}{2} 
             ___
         I*\/ 6 
x2 = 2 + -------
            2
x2=2+6i2x_{2} = 2 + \frac{\sqrt{6} i}{2} 
x2 = 2 + sqrt(6)*i/2
Numerical answer [src] 
x1 = 2.0 - 1.22474487139159*i
x2 = 2.0 + 1.22474487139159*i
x2 = 2.0 + 1.22474487139159*i
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