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