Lynienicole
  • Lynienicole
Hello everyone, is anyone interested in helping me solve a polynomial equation? (Link below is an screenshot of the question) http://prntscr.com/88wws6
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
ill help
anonymous
  • anonymous
r u there girl
Lynienicole
  • Lynienicole
Your help would be much appreciated! :) I'm stuck on question 2

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anonymous
  • anonymous
ok
anonymous
  • anonymous
let me see
anonymous
  • anonymous
im here
anonymous
  • anonymous
u know whats important
Lynienicole
  • Lynienicole
Important regarding to the question? Would be the polynomial, correct?
Lynienicole
  • Lynienicole
Are you still available to help?
anonymous
  • anonymous
yes
anonymous
  • anonymous
hello r u there
Lynienicole
  • Lynienicole
I am still here, do you understand question 2 ? I'm totally confused on how to use the fundamental theorem and Descartes' rules.
amistre64
  • amistre64
define the thrm and the rule
Lynienicole
  • Lynienicole
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
amistre64
  • amistre64
hmm, is that the thrm from your material, or from the internet? just curious
amistre64
  • amistre64
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.
Lynienicole
  • Lynienicole
Google definition. My Teacher/Professor never explained what it was..
amistre64
  • amistre64
ah, google definitions are not always the simplest constructions
Lynienicole
  • Lynienicole
Aha, very true.
amistre64
  • amistre64
https://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html this seems like a much simpler and easier to read description of it
amistre64
  • amistre64
an nth degree poly has n complex roots. but real roots are complex roots of the form: r + 0i
amistre64
  • amistre64
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?
Lynienicole
  • Lynienicole
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"?
amistre64
  • amistre64
use the thrm and the sign rule to show to the foreman that your graph meets the requirements yes
amistre64
  • amistre64
you have an x^3 poly ... 3rd degree, and we have 3 real roots right? so the thrm holds
amistre64
  • amistre64
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 ---------------- then let x be some negative number; -a and do the same process to determine the number of possible negative roots
amistre64
  • amistre64
for simplicity, i just use 1 and -1 for x instead of a and -a
Lynienicole
  • Lynienicole
Thank you so much! Your help was greatly appreciated. :)
amistre64
  • amistre64
your welcome, and good luck

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