Question

What are the possible number of positive, negative, and complex zeros of f(x) = x6 + x5+ x4 + 4x3 – 12x2 + 12 ?

Positive: 4, 2, or 0; Negative: 2 or 0; Complex: 4, 2, or 0

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

Positive: 2 or 0; Negative: 2 or 0; Complex: 4, 2, or 0

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

Answer 1

You have a total of 6 solutions due to the power of 6. My graphing calculator is dead at the moment (no batteries) but look at the graph and see how many times the function crosses the x axis

Answer 2

2 times.

Answer 3

Ok complex solutions come in pairs ie you have to say 2 complex or 4 complex

Answer 4

so... ? answer?

Answer 5

B, orD ?

Answer 6

Let me work it out by hand. I am going to use p/q for possible rational and then synthetic division

Answer 7

Damn, sorry! :(

Answer 8

No do you have a graphing calculator? If so type in your function into the y= screen.

Answer 9

then?

Answer 10

tell me a shortcut if u know any.

Answer 11

your possible solutions are 1, 2, 3, 4, 6, 12
go look at your x values we are looking for your y value to be zero.
Type in -1, +1, -2, +2, -3, +3, +4, -4, +6, -6, +12, -12
Tell me which ones give you y=0 this is where the function croses the x axis and therefore solutions

Answer 12

this is the shortcut

Answer 13

http://www.geogebra.org/webstart/geogebra.html

Answer 14

try that here.

Answer 15

Thanks for all your help.. :)

Answer 16

well I would be happy to do synthetic division except it takes a while.

Answer 17

if u want to see the graph, i can post it here, im not using windows so it takes a while.

Answer 18

that link runs in Mozilla.
you can graph that there.

Answer 19

sorry it would be faster if my graphing calculator wasn't dead. I need to go get some batteries. Maybe I will do this later tonight or tomorrow.

Answer 20

ok, cool. thanks.. :)