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x^2-8*x+17=0

x^2-8*x+17=0 equation

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Numerical solution:

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The solution

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x  - 8*x + 17 = 0
(x2−8x)+17=0\left(x^{2} - 8 x\right) + 17 = 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=1a = 1
b=−8b = -8
c=17c = 17
, then
D = b^2 - 4 * a * c = 

(-8)^2 - 4 * (1) * (17) = -4

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=4+ix_{1} = 4 + i
x2=4−ix_{2} = 4 - i
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−8p = -8
q=caq = \frac{c}{a}
q=17q = 17
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=8x_{1} + x_{2} = 8
x1x2=17x_{1} x_{2} = 17
The graph
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Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 4 - I
x1=4−ix_{1} = 4 - i 
x2 = 4 + I
x2=4+ix_{2} = 4 + i 
x2 = 4 + i
Sum and product of roots [src] 
sum
4 - I + 4 + I
(4−i)+(4+i)\left(4 - i\right) + \left(4 + i\right) 
=
8
88 
product
(4 - I)*(4 + I)
(4−i)(4+i)\left(4 - i\right) \left(4 + i\right) 
=
17
1717 
17
Numerical answer [src] 
x1 = 4.0 - 1.0*i
x2 = 4.0 + 1.0*i
x2 = 4.0 + 1.0*i
The graph
x^2-8*x+17=0 equation
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