# Math Help - Find All Zeros

1. ## Find All Zeros

Find All Zeros.

$f(x) = 3x^3-20x^2+7x+30$

Alright, I applied the Rational Zero Theorem and thought I found these as possibilities:

1,3,10,15,2,30
____________
1,3

Plus or minus: 1, 3, 10, 15, 2, 30, 1/3, 10/3, 5, 2/3.

I tested them all and didn't get anything as far as I know. Now I don't know what to do. I think I'm supposed to find ALL zeros, so that could mean imaginary as well. I know there's at least three zeros, right? How'd I go about working this one out?

2. Originally Posted by A Beautiful Mind
Find All Zeros.

$f(x) = 3x^3-20x^2+7x+30$

Alright, I applied the Rational Zero Theorem and thought I found these as possibilities:

1,3,10,15,2,30
____________
1,3

Plus or minus: 1, 3, 10, 15, 2, 30, 1/3, 10/3, 5, 2/3.

I tested them all and didn't get anything as far as I know. Now I don't know what to do. I think I'm supposed to find ALL zeros, so that could mean imaginary as well. I know there's at least three zeros, right? How'd I go about working this one out?
Hi ABM,

It looks like you left out 6 as a possible zero. I believe -1 works as well.

3. Hey.

Yeah, I figured that out, lol.

For the -1, I had accidently for some reason thought at the end when doing the synthetic divison it was 30+30 instead of 30-30. It's easy to get the zeros with a graphing calculator cause they're x-intercepts I also found out too. That was definitely not said in my Precal book.