Question

Hello everyone, is anyone interested in helping me solve a polynomial equation?

(Link below is an screenshot of the question)

http://prntscr.com/88wws6

Answer 1

ill help

Answer 2

r u there girl

Answer 3

Your help would be much appreciated! :) I'm stuck on question 2

Answer 4

ok

Answer 5

let me see

Answer 6

im here

Answer 7

u know whats important

Answer 8

Important regarding to the question? Would be the polynomial, correct?

Answer 9

Are you still available to help?

Answer 10

yes

Answer 11

hello r u there

Answer 12

I am still here, do you understand question 2 ? I'm totally confused on how to use the fundamental theorem and Descartes' rules.

Answer 13

define the thrm and the rule

Answer 14

The fundamental theorem of algebra states that every polynomial equation over the field of complex numbers of degree higher than one has a complex solution. Polynomials of the form , with a, b,... coefficients real or complex, can be factored completely into where the r, s,... are complex numbers.


In mathematics, Descartes' rule of signs, first described by René Descartes in his work La Géométrie, is a technique for determining an upper bound on the number of positive or negative real roots of a polynomial

Answer 15

hmm, is that the thrm from your material, or from the internet? just curious

Answer 16

the form i am used to is that the degree of a polynomial defines the number of possible real zeros. an nth degree polynomial therefore has at most n real roots.

Answer 17

Google definition. My Teacher/Professor never explained what it was..

Answer 18

ah, google definitions are not always the simplest constructions

Answer 19

Aha, very true.

Answer 20

https://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html

this seems like a much simpler and easier to read description of it

Answer 21

an nth degree poly has n complex roots.

but real roots are complex roots of the form: r + 0i

Answer 22

so accounting for complex roots; the degree of a polynomial tells us that a poly has at most, n real roots for some nth degree.

does this make sense?

Answer 23

I read over the link, and it makes my thinking a lot clearer aha. So basically, for question 2. I create a graph using those two functions, and explain how it matches the "construction foreman"?

Answer 24

use the thrm and the sign rule to show to the foreman that your graph meets the requirements yes

Answer 25

you have an x^3 poly ... 3rd degree, and we have 3 real roots right? so the thrm holds

Answer 26

the sign rule just tells us the possible number of positive and negative roots and its a little complicated depending on your abilities.

let x be some positive number; a

then count the number of times the 'operations' change from + to - and back again

that gives us the number of possible positive roots
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then let x be some negative number; -a and do the same process to determine the number of possible negative roots

Answer 27

for simplicity, i just use 1 and -1 for x instead of a and -a

Answer 28

Thank you so much! Your help was greatly appreciated. :)

Answer 29

your welcome, and good luck