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

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
======================================
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:

RELATED QUESTIONS
May I please have some help solving this equation? Find all solutions of the equation... (answered by stanbon)
Hi. Can I have some help with the following equation Find all real solutions of the... (answered by stanbon)
On the following I always get a no solutions answer, but its noted that their are real... (answered by jim_thompson5910)
Hi. May I have some help finding solutions to the equation? Find all real solutions of (answered by Edwin McCravy)
Hi May I have some help with finding solutions to this equation? Find all real... (answered by Nate)
Hi May I have some help with the following equation? Find all real solutions of the... (answered by stanbon,checkley71)
Hi. May I have some help with the following equation? Find all real solutions of the... (answered by stanbon,checkley71)
Hi. I have a question on the following equation. Find all real solutions of the... (answered by stanbon)
Hello. May I have some help solving this equation? Find all real solutions of the... (answered by checkley71)