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x^4+2x^2+1=0

x^4+2x^2+1=0 equation

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Numerical solution:

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The solution

You have entered [src] 
 4      2        
x  + 2*x  + 1 = 0
(x4+2x2)+1=0\left(x^{4} + 2 x^{2}\right) + 1 = 0
Simplify
Detail solution
Given the equation:
(x4+2x2)+1=0\left(x^{4} + 2 x^{2}\right) + 1 = 0
Do replacement
v=x2v = x^{2}
then the equation will be the:
v2+2v+1=0v^{2} + 2 v + 1 = 0
This equation is of the form
a*v^2 + b*v + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
v1=D−b2av_{1} = \frac{\sqrt{D} - b}{2 a}
v2=−D−b2av_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=2b = 2
c=1c = 1
, then
D = b^2 - 4 * a * c = 

(2)^2 - 4 * (1) * (1) = 0

Because D = 0, then the equation has one root.
v = -b/2a = -2/2/(1)

v1=−1v_{1} = -1
The final answer:
Because
v=x2v = x^{2}
then
x1=v1x_{1} = \sqrt{v_{1}}
x2=−v1x_{2} = - \sqrt{v_{1}}
then:
x1=x_{1} =
01+(−1)121=i\frac{0}{1} + \frac{\left(-1\right)^{\frac{1}{2}}}{1} = i
x2=x_{2} =
01+(−1)(−1)121=−i\frac{0}{1} + \frac{\left(-1\right) \left(-1\right)^{\frac{1}{2}}}{1} = - i
The graph
-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.5020
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -I
x1=−ix_{1} = - i 
x2 = I
x2=ix_{2} = i 
x2 = i
Sum and product of roots [src] 
sum
-I + I
−i+i- i + i 
=
0
00 
product
-I*I
−ii- i i 
=
1
11 
1
Numerical answer [src] 
x1 = 1.0*i
x2 = -1.0*i
x2 = -1.0*i
The graph
x^4+2x^2+1=0 equation
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