A community for students.
Here's the question you clicked on:
 0 viewing
dkoos7
 4 years ago
What are the possible number of positive, negative, and complex zeros of f(x) = 2x3 – 5x2 – 6x + 4 ?
dkoos7
 4 years ago
What are the possible number of positive, negative, and complex zeros of f(x) = 2x3 – 5x2 – 6x + 4 ?

This Question is Closed

Mandolino
 4 years ago
Best ResponseYou've already chosen the best response.2Descartes' Rule of Signs: do you know about it?

dkoos7
 4 years ago
Best ResponseYou've already chosen the best response.0Yea im just confused on how to find how many numbers fall under each of the categories

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.0Well, at first pass, we notice that because of the 2x^3 term, then for large negative x, f(x) is negative and for large positive x, f(x) is positive. So the equation must have at least one zero. I would now differentiate and see if the critical points tell you something about how the function behaves between large negative and large positive values.

Mandolino
 4 years ago
Best ResponseYou've already chosen the best response.2The max number of pos. real roots is the number of sign changes of f... 2 in this case, but that number can be less by a positive even integer, i.e., 22=0.

Mandolino
 4 years ago
Best ResponseYou've already chosen the best response.2So there are 2 or 0 pos. real roots. do you remember the next part? How to get the max number of negative real roots?

Mandolino
 4 years ago
Best ResponseYou've already chosen the best response.2The max number of negative real roots is the number of sign variations of f(x). When you replace x for x in the rule of the function, all the terms with odd powers will change signs: f(x)=2x^35x^2+6x+4 and now there is 1 sign variation, so the number of negative real roots is 1 (this has to be a root remember what james sped earlier? Odd degreed polynomial functions have at least one real root). (put all the info together on next post)

Mandolino
 4 years ago
Best ResponseYou've already chosen the best response.2Pos. Real Neg. Real Complex 2 1 0 0 1 2 the above table summarizes the two possible arrangements of the roots

Mandolino
 4 years ago
Best ResponseYou've already chosen the best response.2A third degree polynomial by a corollary to the Fundamental theorem of Algebra indicates must have 3 roots, and each row shows the 3 arranged by type.

dkoos7
 4 years ago
Best ResponseYou've already chosen the best response.0Thank you! your a life saver! and you know a lot about math lol

Mandolino
 4 years ago
Best ResponseYou've already chosen the best response.2maybe the former... I don't about the latter... it's all relative you know :})
Ask your own question
Sign UpFind more explanations on OpenStudy
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.