Question

ALGEBRA 2


Using complete sentences, describe how you would analyze the zeros of the polynomial function f(x) = 7x^5 + 15x^4 – x^3 + 4x^2 – 6x – 11 using Descartes’ Rule of Signs. Be sure to provide the answer in your explanation.

Answer 1

why are you studying algebra 2?

Answer 2

what do you mean why? i did NOT fail it, i'm trying to get ahead so i'm taking it online but i don't understand this problem.

Answer 3

do you like math?

Answer 4

uh, sure? can you help me with this question?!

Answer 5

of course

Answer 6

so,

Answer 7

do you plan to be mathematician?

Answer 8

ok dude i'm tired of this. bye.

Answer 9

alrigh i will help

Answer 10

now, what do you know about the descartes rule of signs?

Answer 11

Yes. I answered like 10 other questions about it but this one I tried and I got a ridiculous answer! I got 3 or 1 real positive, 4 or 2 real negative, and i didnt get an answer for complex.

Answer 12

so, you do know something, thats good, at least your not just trying to cheat

Answer 13

lets begin

Answer 14

is my answer right though? and there is 0 possibility for complex.

Answer 15

so, how many sign changes do we have in f(x), i count 3

Answer 16

i count 3. and then subtract 2, so 3 or 1 possible positive.

Answer 17

now, when we substiute in -x what do we get, how many sign changes? i count 2 right?

Answer 18

so 3 positve real roots can exist, and 2 negative real roots

Answer 19

I counted 4? but thats the trouble i am having, what do you do in the sign changes? can you please step by step do sign changes? because i got (after the sign change) f(-x) = -7x^5 - 15x^4 + x^3 - 4x^2 + 6x - 11.

Answer 20

okay, so we have orginal f(x)=7x^5 + 15x^4 – x^3 + 4x^2 – 6x – 11 right?

i count 3 sign changes

Answer 21

Yes...

Answer 22

now when i replace with -x, we have f(-x)=–7x5 + 15x4 + x3 + 4x2 + 6x – 11, right?

here i count 2 changes

Answer 23

thus: 3 positve real roots can exist, and 2 negative real roots

Answer 24

why did you only replace 7x5 and x3 and 6x? are you supposed to skip one each time or do it as binomials or something?

Answer 25

why, b/c look at the exponets, if i put a negative number in x^2 it will come out positive. If i put a negative number in x^3 it will still be negative.

Answer 26

get it?

Answer 27

If i place a negative number in:
even exponets=positive
odd expoent=negative

Answer 28

Ok! I see now, alright thanks!

Answer 29

thats right you just got owned

Answer 30

jk