Question

What are the solutions of the equation x4 + 3x2 + 2 = 0? Use u substitution to solve. mc018-1.jpg and x = ±1 mc018-2.jpg and x = ±i mc018-3.jpg and x = ±i mc018-4.jpg and x = ±1

Answer 1

C-0, D-2, E-4

Explanation:

I got it wrong and it gave me this answer!

Answer 2

ANSWER


`x = \pm \: i`
or


`x = \pm \: √(2) i`

EXPLANATION

We want to solve the equation,


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

We rewrite the equation to get,


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

We can now let

`y = {x}^(2)`

We substitute this value to get,


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

We factor this to get,


`(y + 1)(y + 2) = 0`

This implies that,


`y = - 1`
or


`y = - 2`

But

`x = \pm \: √(y)`

Thus implies that,


`x = \pm \: √( - 1)`

`\Rightarrow x = \pm \: i`

or


`x = \pm \: √( - 2)`


`\Rightarrow x = \pm \: √(2) i`