Question

Please Help!
What are the possible number of positive, negative, and complex zeros of f(x) = x^6 - x^5- x^4 + 4x^3 - 12x^2 + 12 ?

a.Positive: 4, 2, or 0; Negative: 2 or 0; Complex: 6, 4, 2, or 0

b.Positive: 3 or 1; Negative: 3 or 1; Complex: 4, 2, or 0

c.Positive: 3 or 1; Negative: 2 or 0; Complex: 4, 2, or 0

d.Positive: 2 or 0; Negative: 2 or 0; Complex: 6, 4, or 2

Answer 1

you can use Descarte's rule of signs here

Answer 2

A plot of f(x) is attached.

Answer 3

you do not need to plot this

Answer 4

@egchick954 are you familiar with Descartes rule of signs?

Answer 5

No I'm not, what is that?

Answer 6

so what method(s) do you think you are supposed to use in order to answer this question?
what has your teacher taught you on this topic?

Answer 7

http://www.purplemath.com/modules/drofsign.htm

Answer 8

Well I think we are supposed to learn that rule you were speaking of but I don't remember what it is exactly. I will check out the link robtobey provided.

Answer 9

@egchick954
I don't remember the rule myself. Don't hesitate to use a Google search like
"Descartes rule of signs" in this case.

Answer 10

okay thank you so much, that will help me a lot.

Answer 11

here is a very good youtube video on it: http://www.youtube.com/watch?v=5YAmwfT3Esc

Answer 12

Thank you so much asnaseer and robtobey!

Answer 13

if you are still stuck after watching that then let me know and I'll guide you on how to use this rule.

Answer 14

yw :)