Question

What are the solutions of the equation x4 + 6x2 + 5 = 0? Use u substitution to solve.

Answer 1

x = ± i and x = ± i√5

Explanation:

hope that helped! It should be answer B!

Answer 2

`x=-i, x=i , x= - √(5) i, x= √(5) i`

EXPLANATION

The given quartic equation is

`{x}^(4) + 6 {x}^(2) + 5 = 0`

We can rewrite this as:

`({x}^(2) )^(2) + 6( {x}^(2) ) + 5 = 0`

Let

`u = {x}^(2)`

Then,

`{u}^(2) + 6 {u} + 5 = 0`

Factor to obtain:

`(u + 1)(u + 5) = 0`

`u = - 1 \: or \: u = - 5`

This implies that,

`{x}^(2) = - 1 \: or \: {x}^(2) = - 5`

`{x}= \pm \: √( - 1) \: or \: {x} = \pm √( - 5)`

`{x}= \pm \: i\: or \: {x} = \pm √( 5) i`

`x=-i, x=i , x= - √(5) i, x= √(5) i`