Question

how would you find the solutions for..

x^4 - 16 = 0

Answer 1

Add 16 to both sides. Then raise both sides to the 1/4 th power

Answer 2

Don't forgot \(\pm\), though.

Answer 3

factor for sure.
(x + 2)(x-2)(x+4)=0

Answer 4

Actually it's (x-2) (x+2) (x²+4).

Answer 5

Think of x^4 - 16 = 0 as
(x^2)^2 - 4^2 = 0
and factor using the difference of two squares.
Then factor the difference of two squares again.

Answer 6

I don't believe (x+4) will work x=-4 -4^4 -16=0 ??????

Answer 7

\[(x-2)(x+2)(x^2+4)\]

Answer 8

Please disregard my solution as I erred.

Answer 9

@geerky42, you are correct it is x^2+4 giving you the complex roots.

Answer 10

So \(\Large x^4 - 16 = (x-2)(x+2)(x-2i)(x+2i) = 0\)

So there are four solutions. (two real and two complex)

x - 2 = 0
x + 2 = 0
x - 2i = 0
x + 2i = 0

\(x = 2, ~-2, ~2i, ~\text{or}~-2i\)

Answer 11

Is this clear? @McKailaMarie2014

Answer 12

yes. thank you!

Answer 13

Glad we helped.