Question

HELP PLEASE! AWARDING METAL. How could you use Descartes' rule and the Fundamental Theorem of Algebra to predict the number of complex roots to a polynomial as well as find the number of possible positive and negative real roots to a polynomial?

Answer 1

hi!!

Answer 2

any particular polynomial?

Answer 3

no.

Answer 4

oh then they just want some kind of "essay" i guess
what a drag

Answer 5

100 words... ugh.

Answer 6

Fundamental Theorem of Algebra says a polynomial of degree n has n roots, but they can be real, complex, or repeated

Answer 7

for example \((x-1)^2\times (x^2+1)\) had degree 4, but the root \(1\) is repeated ,and the other two are complex \(i,-i\)

Answer 8

Oh, ok.

Answer 9

descartes rule of sign is easy to use not so easy to explain in words, read the purplemath link sent above
basically you look at the changes in sign of \(p(x)\)
if there are 4 changes in sign there are either 4, 2 or no positive roots, if there are say 5 changes in sign then there are 5 , 3 , or 1 positive roots
you count down by twos

Answer 10

then look at the changes in sign of the coefficients for \(p(-x)\)and it is the same story only for negative roots

Answer 11

it might not even be clear what i mean by "changes in sign of the coefficients'
read the purplemath stuff, might make it easier

Answer 12

Oh, ok.

Answer 13

it would be a lot easier to do an example, but you are not asked for one, so just say a bunch of words

Answer 14

btw your friend is cute (i assume that is not "johnny")

Answer 15

Johnny's my BF, lol.

Answer 16

\[\color\magenta\heartsuit\]

Answer 17

Lol, :)

Answer 18

Choice #1: Describe each of the following properties of the graph of the Cosine Function, f(theta) = cos(theta) and relate the property to the unit circle definition of cosine.

Amplitude
Period
Domain
Range
x-intercepts

Answer 19

Is this one ok?

Answer 20

hold on

Answer 21

another essay question?

Answer 22

yeah.

Answer 23

you gotta do both??

Answer 24

yea, Lol.

Answer 25

yikes

Answer 26

you have no idea, Lol...

Answer 27

can you pad out the first one with what i wrote plus the stuff from purplemath?

Answer 28

Oh sure, bathroom break... Sorry!

Answer 29

k ttyl

Answer 30

back.
Now how Do you want me to pad out your stuff.

Answer 31

if it was me i would do this,
i would make up an example

Answer 32

& the stuff from purplemath.

Answer 33

Oh, ok.

Answer 34

So you want me to write out the essay, pretty much.

Answer 35

For like Revision.

Answer 36

you can copy down the stuff i wrote, then make up an example where there are say 2 positive root,s one negative roots, and two complex roots
then show how it works
don't forget the complex roots come in pairs, so there has to be an even number of them

Answer 37

Ok, one minute

Answer 38

Do I really need an example?