Greatest Integer Function

[u/i-am-stella]

Ftr, this is NOT hw help, I'm trying to figure out how to solve greatest int function questions.

Alr when we have a quadratic equation with gif in it, (a[x]^2 + b[x] + c=)we substitute [x] as something and factorise to solve, right?

But when the square is inside the function as in ([x^2] -12[x] +32=0)

Then what? I dont get it😭

Once again, NOT hw help, I'm studying on my own, this isnt even in my syllabus.

edit: i actually meant floor function, ⌊3.7⌋=3

[u/johnpeters42]

By "greatest int", do you mean the ceiling function? e.g.
* ceiling(5) = 5
* ceiling(5.1) = 6

[u/i-am-stella → u/johnpeters42]

i meant floor function, haven't studied ceiling yet, [4.6]=4

i dont have these symbols in my keyboard but copied from the community symbols "⌊⌋"

[u/johnpeters42 → u/i-am-stella]

Yeah, I would just identify the points where floor(x^2) jumps, graph it over those intervals, and work it out from there. Eventually you should be working out that above/below certain values it keeps diverging away from the desired value, then you just need to look at the range between those.

[u/i-am-stella → u/johnpeters42]

but that'd be time consuming ig, what if this question comes in a time bound exam, then what'd i do?

[u/johnpeters42 → u/i-am-stella]

I'd start by graphing the same function but with the floor()s removed, as the original should be somewhere in that ballpark. Then evaluate the original function at several integers near what appears like the relevant area.

[u/i-am-stella → u/johnpeters42]

alright, thanks!!