Question

What are the solutions of the equation x^4+3x^2+2=0

Answer 1

ANSWER


`x = \pm \: √(2) i \: \: or \: \: x = \pm i`

Step-by-step explanation

The given equation is

`{x}^(4) + 3 {x}^(2) + 2 = 0`


We can rewrite this in the form,


`( {x}^(2) ) ^(2) + 3 {x}^(2) + 2 = 0`


We can think of this as a quadratic equation in

`{x}^(2)`


We split the middle term with 2 and 1 to obtain,



`( {x}^(2) ) ^(2) + {x}^(2) + 2{x}^(2) + 2 = 0`


We factor to obtain,




`{x}^(2) ( {x}^(2) + 1) + 2( {x}^(2) + 1) = 0`



`({x}^(2) + 2)( {x}^(2) + 1) = 0`





`{x}^(2) = - 2 \: \: or \: \: {x}^(2) = - 1`




`x = \pm \: √(2) i \: \: or \: \: x = \pm i`