The function below has at least one rational zero.
Use this fact to find all zeros of the function.

g(x)=3x^4-8x^3+4x^2-x+2
If there is more than one zero, separate them with commas. Write exact values, not decimal approximations.

Question

The function below has at least one rational zero. 
Use this fact to find all zeros of the function.

g(x)=3x^4-8x^3+4x^2-x+2 
If there is more than one zero, separate them with commas. Write exact values, not decimal approximations.

anonymous · Answer

I get rational zeros $$\pm1,\pm \frac{ 1 }{ 3 }, \pm2,\pm \frac{ 2 }{ 3 }$$

terenzreignz · Answer

These are the POSSIBLE rational zeros.  You need to plug them in and check them...

anonymous · Answer

So I get 1,2, 11i, -11i is that correct?

terenzreignz · Answer

Hang on  :D
So, you're right about 1 and 2... how did you get 11i and -11i  ?
Serious question by the way... I'm terrible at division of polynomials o.O

anonymous · Answer

using synthetic division to find the real zeros I got:  1/6 (-1-sqrt11) and 1/6(-1+sqrt11)

anonymous · Answer

which is a complex root

terenzreignz · Answer

My calculator says you're right :D

anonymous · Answer

So should I include the complex root in my answer? 1,2, -1/6(11i), and 1/6(11i)

anonymous · Answer

what calculator? Can I buy it?  :D

terenzreignz · Answer

Yes.  They said all the zeros, not just the rational zeros. (or real zeros, for that matter)
It's a Casio calculator.  I'm sure it's available somewhere in your vicinity.
I asked it to (LOL) find the roots of the equation
3x² + x + 1
And it jives with your answers :D

anonymous · Answer

I'm doing the "Aleks" assessment.  Just don't know how to insert the answer so it will read it the right way.

terenzreignz · Answer

whoop-de-doo
Can't help you in that regard, mate :D
Cheers ;)

anonymous · Answer

thanks

anonymous · Answer

@amistre I just want to post this the right way. 1,2, $$\frac{ 1 }{ 6 }(-1\pm i \sqrt{11})$$ Is that the right way to write the complex root or should I separate it,i.e. $$\frac{ 1 }{ 6 }(-1-i \sqrt{11}), \frac{ 1 }{ 6 } (-1+i \sqrt{11})$$

anonymous · Answer

@amistre64 , @Mertsj

mertsj · Answer

Don't they give instructions about the correct way to report answers?

amistre64 · Answer

Use this fact to find $\underline{ALL}$ zeros of the function.  If it had stipulated all REAL zeros then we would omit the complex ones

anonymous · Answer

Gotcha!

amistre64 · Answer

pfft, formating eh ... thats up to the program

anonymous · Answer

I know right!

amistre64 · Answer

separate them with commas, so second option

anonymous · Answer

but is it typical to put the plus/minus sign into the answer or do you normally separate it?

anonymous · Answer

Got it- thank you guys!

amistre64 · Answer

mathically, its the same .... programically ... it matters

anonymous · Answer

I see said the mathmatically blind man.

anonymous · Answer

You guys are the best- thanks again.