Mister Exam

Other calculators


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

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

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src]
 4      2        
x  + 2*x  + 1 = 0
$$\left(x^{4} + 2 x^{2}\right) + 1 = 0$$
Detail solution
Given the equation:
$$\left(x^{4} + 2 x^{2}\right) + 1 = 0$$
Do replacement
$$v = x^{2}$$
then the equation will be the:
$$v^{2} + 2 v + 1 = 0$$
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:
$$v_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$v_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 2$$
$$c = 1$$
, 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)

$$v_{1} = -1$$
The final answer:
Because
$$v = x^{2}$$
then
$$x_{1} = \sqrt{v_{1}}$$
$$x_{2} = - \sqrt{v_{1}}$$
then:
$$x_{1} = $$
$$\frac{0}{1} + \frac{\left(-1\right)^{\frac{1}{2}}}{1} = i$$
$$x_{2} = $$
$$\frac{0}{1} + \frac{\left(-1\right) \left(-1\right)^{\frac{1}{2}}}{1} = - i$$
The graph
Sum and product of roots [src]
sum
-I + I
$$- i + i$$
=
0
$$0$$
product
-I*I
$$- i i$$
=
1
$$1$$
1
Rapid solution [src]
x1 = -I
$$x_{1} = - i$$
x2 = I
$$x_{2} = i$$
x2 = i
Numerical answer [src]
x1 = 1.0*i
x2 = -1.0*i
x2 = -1.0*i
The graph
x^4+2*x^2+1=0 equation