Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

timo86m

T or F any 3rd degree polynomial has at at least one real root?

  • one year ago
  • one year ago

  • This Question is Closed
  1. cherylim23
    Best Response
    You've already chosen the best response.
    Medals 0

    True, can you explain why?

    • one year ago
  2. Skvadlamudi
    Best Response
    You've already chosen the best response.
    Medals 0

    True

    • one year ago
  3. ash2326
    Best Response
    You've already chosen the best response.
    Medals 2

    Yeah @timo86m , but the third degree polynomial should have real coefficients

    • one year ago
  4. timo86m
    Best Response
    You've already chosen the best response.
    Medals 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
  5. cherylim23
    Best Response
    You've already chosen the best response.
    Medals 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 non-constant single-variable 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
  6. timo86m
    Best Response
    You've already chosen the best response.
    Medals 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
  7. satellite73
    Best Response
    You've already chosen the best response.
    Medals 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
  8. timo86m
    Best Response
    You've already chosen the best response.
    Medals 0

    good point

    • one year ago
    • Attachments:

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.