Find all zeroes of a polynomial!

[lightfight]

I'm having trouble with this problem: Find all zeroes of:
f(x)=x^4 - 3x^3 + 3x^2 +5x - 12

I've tried dividing by all the factors: 1,2,3,4,6,12 and their negatives with no zeroes found. I looked at the graph and it does cross but at fractions. What am I supposed to do?

 

[galactus]

This has two real and 2 non-real zeros. These can be boogers to find the zeros. Especially, when the zeros may be irrational.

This thing isn't nicely factorable.

I don't know if that's allowed or not, but I would use tech.

\(\displaystyle \L\\x=1.82744894433...., \\ -1.43181024483...., \\ 1.30218065025-1.70014692205i, \\ 1.30218065025+1.70014692205i\)

 

[lightfight]

I'm allowed to use graphs, but I don't know if he will accept decimals as answers. The problems we had before came out much nicer than this.

I understood the first two parts of your answer, gotten from a graph. But where did you get the last two? The "complex" numbers.

 

[galactus]

Actually, I was lazy and ran it through my TI-92.

Maybe you're just required to identify the roots. 2 real and 2 complex. You can Descartes rule of signs for that.