Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

cherylim23Best ResponseYou've already chosen the best response.0
True, can you explain why?
 one year ago

ash2326Best ResponseYou've already chosen the best response.2
Yeah @timo86m , but the third degree polynomial should have real coefficients
 one year ago

timo86mBest ResponseYou've already chosen the best response.0
yes i can @cherylim23 because x^2 has u or n shape but 3rd degree has a dw:1342235273380:dw shape
 one year ago

cherylim23Best ResponseYou've already chosen the best response.0
Condition i s that all coefficients are real. Do you know why? This relates back to the fundamental theorem of algebra, which states that every nonconstant singlevariable polynomial with complex coefficients has at least one complex root. However, if the coeffients are all real, you can apply the complex conjugate theorem here, leaving you definitely one real root at least since all complex roots would have occured in conjugate pairs. Bit hard to understand if you haven't learnt complex numbers yet, but just keep this in mind
 one year ago

timo86mBest ResponseYou've already chosen the best response.0
i know basic complex numbers like a HS level knowledge of them. But I know if it is all real then a shape like dw:1342235527228:dw should always intersect the x axis at least once. in a u or n shaped graph due to a 2nd dagree polynomial there are ways to shift the curve up or down so that it never intersects the x axis.
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
another reason is that the complex roots come in conjugate pairs, so you cannot have just one of them or three of them
 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.