Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Help? Using complete sentences, describe how you would analyze the zeros of the polynomial function f(x) = –3x^5 – 8x^4 +25x^3 – 8x^2 +x – 19 using Descartes’ Rule of Signs.
 one year ago
 one year ago
Help? Using complete sentences, describe how you would analyze the zeros of the polynomial function f(x) = –3x^5 – 8x^4 +25x^3 – 8x^2 +x – 19 using Descartes’ Rule of Signs.
 one year ago
 one year ago

This Question is Closed

jim_thompson5910Best ResponseYou've already chosen the best response.1
in f(x), how many sign changes are there?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
notice that going from 8x^4 to +25x^3, there's a sign change from negative to positive
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
do you see this?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
ok there's another from +25x^3 to 8x^2
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
what's another one?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
there's one more
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
from 8x^2 to +x
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
so there are 4 sign changes total in f(x)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
this means that there are at most 4 positive real roots
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
no that's the same sign change (just in reverse)
 one year ago

P.nut1996Best ResponseYou've already chosen the best response.0
4 sign changes=4 positive real roots
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
at most 4 (there could be 0, 1, 2, 3, or 4 positive real roots)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
4 is the maximum
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
now we must find f(x)
 one year ago

P.nut1996Best ResponseYou've already chosen the best response.0
I'm still really confuzzled...
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
the rule is if f(x) has n sign changes, then there are AT MOST n positive real roots
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
if n = 4, then if f(x) has 4 sign changes, then there are AT MOST 4 positive real roots
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
making more sense?
 one year ago

P.nut1996Best ResponseYou've already chosen the best response.0
I don't know how to formulate an answer from you telling me this...
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
you don't need to find the actual roots you just need to be able to count the possible number and type
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
more specifically, how many positive real roots you could have (in this case, at most 4) you don't need to find the 4 or find out how many actual positive roots there are
 one year ago

P.nut1996Best ResponseYou've already chosen the best response.0
But I need a definite answer, right?
 one year ago

P.nut1996Best ResponseYou've already chosen the best response.0
I can't just say "maybe 4"?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
well that's part of the answer, we still have to find f(x)
 one year ago

P.nut1996Best ResponseYou've already chosen the best response.0
Okay, and how would we go about that ? :)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
start with f(x) then replace each x with x and simplify
 one year ago

P.nut1996Best ResponseYou've already chosen the best response.0
Could you give me an example?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
start with this f(x) = –3x^5 – 8x^4 +25x^3 – 8x^2 +x – 19 then replace each 'x' with 'x' to get f(x) = –3(x)^5 – 8(x)^4 +25(x)^3 – 8(x)^2 +(x) – 19 then simplify to get ???
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
does that help?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
ok what do you get
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
when you simplify
 one year ago

P.nut1996Best ResponseYou've already chosen the best response.0
3x^5=f(x)+x(x(x8x(+25)+8)+1)+19??
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
f(x) = –3(x)^5 – 8(x)^4 +25(x)^3 – 8(x)^2 +(x) – 19 would simplify to f(x) = 3x^5 – 8x^4  25x^3 – 8x^2  x – 19
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
now count the sign changes in f(x) = 3x^5 – 8x^4  25x^3 – 8x^2  x – 19 and tell me how many you got
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
3x^5 is the same as +3x^5
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
so there's only one sign change from +3x^5 to 8x^4
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
so this means that there is at most 1 negative real root
 one year ago

P.nut1996Best ResponseYou've already chosen the best response.0
Oh, I was just looking at it wrong.. Sorry :(
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
So far we found that there are at most 4 positive real roots and at most 1 negative real root
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
so one possibility is that there are 4+1 =5 real roots (4 positive, 1 negative) BUT this is not the only possibility
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
we could have 3 positive real roots and 1 negative real root to have 3+1 = 4 real roots total but the problem with this scenario is that you would only have 51 = 1 complex root...when complex roots should come in pairs
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
so that scenario of 3 positive real roots and 1 negative real root just isn't possible
 one year ago

P.nut1996Best ResponseYou've already chosen the best response.0
Okay So don't worry about the last scenario?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
anyways, there are a ton of possibilities the good news is that you can sum them all up by saying there are at most 4 positive real roots (you could have 0, 1, 2, 3, or 4 positive real roots) there is at most 1 negative real root (you could have 0 or 1 negative real roots) there are at most 5 complex roots (if there are no real roots at all)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
in short there are at most 4 positive real roots there is at most 1 negative real root there are at most 5 complex roots
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
we can stop there because we don't need to find the actual roots or the counts of the types or roots...just the max of all of the possible types of roots
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.