Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
HelpMe94
Group Title
Use the Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function:
f(x)= 5x^3+X^2X+5
 2 years ago
 2 years ago
HelpMe94 Group Title
Use the Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function: f(x)= 5x^3+X^2X+5
 2 years ago
 2 years ago

This Question is Closed

mathmate Group TitleBest ResponseYou've already chosen the best response.1
How many times did the expression changed sign?
 2 years ago

mathmate Group TitleBest ResponseYou've already chosen the best response.1
There is then a MAXIMUM of 3 positive roots, but it could also be 1.
 2 years ago

mathmate Group TitleBest ResponseYou've already chosen the best response.1
Now flip the sign of the coefficients of the odd powers. How many times does the new expression change sign?
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
Is that 5X^3+X^2+X+5
 2 years ago

mathmate Group TitleBest ResponseYou've already chosen the best response.1
The number of sign changes is the maximum number of positive roots, including complex. If there are two complex roots (as is the case), then there is only one (real) positive root.
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
so the negative right converted right?
 2 years ago

mathmate Group TitleBest ResponseYou've already chosen the best response.1
Yes, the number of sign changes of the new expression (i.e. replace x by x) gives the MAXIMUM number of negative roots.
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
So for this one there is none for the negative and 1 for the positive
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
so how do you know there is one and not 3 for the positive?
 2 years ago

mathmate Group TitleBest ResponseYou've already chosen the best response.1
Using the Descartes rule of signs, we do know that there is no negative root. But we do not know if there is ONE or THREE positive roots.
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
ok so the answer for positive is 1 and 3 and negative is 0
 2 years ago

mathmate Group TitleBest ResponseYou've already chosen the best response.1
You can find that out by factoring the expression. A cubic has at least one real root, and we know that it is positive in this case.
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
one other question:
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
Use the Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function: f(x)=3X^2+2X^2+x+3
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
how does this work then?
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
the positive looks like there is none and same with the negative?
 2 years ago

mathmate Group TitleBest ResponseYou've already chosen the best response.1
Now, let's see. (1) The expression as is has no change in sign, so what do you conclude? (2) flip the sign of the odd powers to give 3X^3+2X^2x+3, sign changed 3 times, what do you conclude?
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
wait why is 3X^2 flipped?
 2 years ago

mathmate Group TitleBest ResponseYou've already chosen the best response.1
I supposed you have a typo! It's 3x^3, ... or not?
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
let me see...
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
oh srry your right
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
Use the Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function: f(x)=3X^3+2X^2+x+3
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
ok so the positive is none then the negative is 3X^3+3X^2X+3, so 2 and 1
 2 years ago

mathmate Group TitleBest ResponseYou've already chosen the best response.1
No positive is correct. Can you repeat the conclusion for negative?
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
i don't understand
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
of so negative is 3 and 1
 2 years ago

mathmate Group TitleBest ResponseYou've already chosen the best response.1
The number of possible roots always differ by an even number because complex roots, if any, come in pairs. 1 and 2 will not be correct. 1 and 3 would be.
 2 years ago

mathmate Group TitleBest ResponseYou've already chosen the best response.1
Perhaps more exactly, 1 OR 3.
 2 years ago

HelpMe94 Group TitleBest ResponseYou've already chosen the best response.0
ok thanks that makes sense
 2 years ago

mathmate Group TitleBest ResponseYou've already chosen the best response.1
You're welcome! :)
 2 years 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.