factoring polynomial 2x^4 = 16x

[mrnerd]

I started out doing this problem, and got 2 of the answers correct. However in the back of my book there is 1 more answer, and I don't understand it.
2x^4 = 16x

2x^4 - 16x = 0

2x(x^3 - 8)

x = 0, x = 2, (and the 2 answers I don't understand) x = -1 + i*sqrt(3), -1 - i*sqrt(3)
I just don't understand where the imaginary answers came from.
Thanks for your help

 

[Deleted member 4993]

I started out doing this problem, and got 2 of the answers correct. However in the back of my book there is 1 more answer, and I don't understand it.
2x^4 = 16x

2x^4 - 16x = 0

2x(x^3 - 8)

x = 0, x = 2, (and the 2 answers I don't understand) x = -1 + i*sqrt(3), -1 - i*sqrt(3)
I just don't understand where the imaginary answers came from.
Thanks for your help

x^3 - 8 = x^3 - 2^3 = (x - 2)(x^2 + 2x + 4)

That will give you the complex roots.

 

[mrnerd]

thank you so much!