SOLUTION: Find all solutions of the equation below. (If there are more answer boxes than answers, enter NONE in the extra boxes.) x4 - 4096 = 0 x = (smaller real solution) x = (larger

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Question 178605: Find all solutions of the equation below. (If there are more answer boxes than answers, enter NONE in the extra boxes.)
x4 - 4096 = 0
x = (smaller real solution)
x = (larger real solution)
x = (smaller imaginary part)
x = (larger imaginary part)
i dont understand! could someone help explain it to me thanks!!!
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
x^4 - 4096 = 0
x^4 - 2^12 = 0
Factor to get:
(x^2-2^6)(x^2+2^6) = 0
Factor to get:
(x-2^3)(x+2^3)(x+8i)(x-8i) = 0
x = 8 or x = -8 or x = -8i or x = 8i
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Cheers,
Stan H.

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

First thing to notice is that you have the difference of two squares:

, so you can factor:

Using the Zero Product Rule:

, or

If , then we can again factor the difference of two squares:

and we have our two real roots, namely 8 and -8.

On the other hand, if , then so which is to say giving us our conjugate pair of complex roots.

In order, your answers should be: