SOLUTION: What are the solutions of the equation x4 + 3x2 + 2 = 0? Use u substitution to solve.

Question 1045527: What are the solutions of the equation x4 + 3x2 + 2 = 0? Use u substitution to solve.
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
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What are the solutions of the equation x4 + 3x2 + 2 = 0? Use u substitution to solve.
~~~~~~~~~~~~~~~~~~~~~~~~~~

 = .


Introduce a new variable u = .

Then your original equation takes the form

 = .

Factor the left side:

(u+1)*(u+2) = 0.

The solutions of this equation are


a)  u = -1, which means  = -1.  This equation has no real solutions.
            It has two complex solutions  x = i  and  x = -i, where i = .


a)  u = -2, which means  = -2.  This equation has no real solutions.
            It has two complex solutions  x =   and  x = .


Answer.  There is no real solutions.
         There are four complex solutions  x = i,  x = -i,  x =   and  x =

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