ANSWER
[tex]x=-i, x=i , x= - \sqrt{5} i, x= \sqrt{5} i[/tex]
EXPLANATION
The given quartic equation is
[tex] {x}^{4} + 6 {x}^{2} + 5 = 0[/tex]
We can rewrite this as:
[tex]({x}^{2} )^{2} + 6( {x}^{2} ) + 5 = 0[/tex]
Let
[tex]u = {x}^{2} [/tex]
Then,
[tex] {u}^{2} + 6 {u} + 5 = 0[/tex]
Factor to obtain:
[tex](u + 1)(u + 5) = 0[/tex]
[tex]u = - 1 \: or \: u = - 5[/tex]
This implies that,
[tex] {x}^{2} = - 1 \: or \: {x}^{2} = - 5[/tex]
[tex]{x}= \pm \: \sqrt{ - 1} \: or \: {x} = \pm \sqrt{ - 5} [/tex]
[tex]{x}= \pm \: i\: or \: {x} = \pm \sqrt{ 5} i[/tex]
[tex]x=-i, x=i , x= - \sqrt{5} i, x= \sqrt{5} i[/tex]
Answer:
x = ± i and x = ± i√5
Step-by-step explanation:
hope that helped! It should be answer B!
