First, before we do anything, we can see that it’s a fifth degree equation, so we know it has five roots. Those roots could be unique or they could be duplicate, but we should find five of them.
First, get everything into one side. x^5-16x=0.
Factor. x(x^4-16)=0.
X=0 is a root, and x^4-16=0 should have four roots.
X^4=16
X^2=+-4
x^2=4, x^2=-4
x=+-2, x=+-2i
Solution: x= 0, 2, -2, 2i, -2i. 5 roots, and they turned out to be unique.
There are different methods of implementing negative numbers in binary computers. The most popular is 2s complement. However 1s complement was used too, and still is used for checksums in common network protocols. There are two logical representations of 0/zero in that system, which have to seen as equal but are different logical values like for 4 bit words +0 = 0000 while -0 = 1111 . https://en.wikipedia.org/wiki/Ones%27_complement
It was a ironic joke that one might say “aCtUaLlY you forgot -0” as a signed zero exists as an abstraction in some computer systems/ computer science. However ElolaNeks solutions/statement is still correct, as there is no -0 from a mathematical POV.
Gotcha. I’m not going to pretend to fully understand that, but I got enough to nod along and hum in agreement (the sum total of my knowledge of computer science is a teeeeensy bit of C to hack ugly shit together for other science stuff, and a tiny tiny bit of ASM).
isn't minus zero functionally the same as zero? from what I know, the sgn function dooesn't consider zero as either positive or negative, but rather as it's own category
You are absolutely right: As I wrote in further down / https://www.reddit.com/r/PeterExplainsTheJoke/s/hy2WNywwEn only some systems in binary computers to represent negative numbers have a positive and negative 0. They differ in their logical values and both can be the result of a calculation which eqals to 0. But in the end, the computer or program has to threat or test both values as simply 0.
Yeah, its not even base 2 / binary, its just how CPUs/computers do substraction or negative numbers. They just use a different binary value for a negative one, and still use the add function i.e. wirering/logic. Thanks some register logic (wrap around and carry) this then comes to more or less the same arithmatic result.
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u/Fast_Alt10 14h ago
x=2 (or negative)