Question

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

Answer 1

ANSWER

$x = \pm \: \sqrt{2} i \: \: or \: \: x = \pm i$

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,



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


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




${x}^{2} = - 2 \: \: or \: \: {x}^{2} = - 1$



$x = \pm \: \sqrt{2} i \: \: or \: \: x = \pm i$