Question

Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.

f(x) = 3x3 + 39x2 + 39x + 27

Answer 1

The very first and easiest thing, even before you get into finding the zeros, is see if there is a factor by which you can simplify the coefficients. In this case, there is, and it makes the problem easier to deal with.

Answer 2

Would the factor be 3? or...

Answer 3

Yes, you can factor out the 3. As for the rest of the problem, if x is positive and real, there are no sign changes going from left to right, so there are no positive real zeros.

Answer 4

If you then look at negative real solutions, there are 3 sign changes, so there are 3 or 3-2=1 negative real solutions.

Answer 5

@tcarroll010 You are not answering the question.....

Answer 6

Alright, so that leaves us with 1 negative real solution but.. how exactly do i tell what my rational 0 list is?
3(x^3 + 13x^2 + 13x + 9)

Answer 7

Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.

Answer 8

I've looked at and read the theorem before, it just really confuses me, could I get an explanation of how you use it?

Answer 9

http://www.cliffsnotes.com/study_guide/Rational-Zero-Theorem.topicArticleId-257309,articleId-257204.html

Answer 10

The above link gives a good concise (emphasis on concise) way to understand and use the theorem. I simply went beyond the problem so as to give insight into zeros. I suggest starting with the rational zeros candidate list and then you could optionally move on to my additional treatment of the problem.

Answer 11

Say you have ax^n + .......+ b

Then you want plus7minus factor combos of b/a (in lowest terms)

In this case, 27/3 is 9/1 so +9/1,-9/1 ,3/1,-3/1, 1/1,-1/1

Answer 12

Ah, that makes a ton more sense

Answer 13

That is indeed the list of rational zeros. If you then want to find the actual zeros (optional and not part of the given problem), you can use my comments to whittle down the list so as to avoid unnecessary work.

Answer 14

Thank you to the both of you. They were both extremely helpful :)

Answer 15

Your function might look like one or the other graphs. Remember, no positive real zeros. So, once you get your rational zero list, you could throw out the positive ones if you are then trying to find the actual zeros.