A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=2 and x=0, and a root of multiplicity 1 at x=−3 Find a possible formula for P(x). I understand what multiplicity is, my question would be is that it says BOTH x=2 and x=0 have a multiplicity of 2, that doesnt make any sense to me.

  • This Question is Closed
  1. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    HI!!

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

    Hello!

  3. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    if 0 is a zero with "multiplicity 2" that means one factor is \(x^2\)

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

    but 2 is also a zero that has a factor of x^2, right?

  5. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no

  6. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    since 2 is a zero, one factor is \(x-2\)

  7. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    since it is a zero with "multiplicity" 2 there are two of those factors, i.e. \((x-2)^2\)

  8. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do you know what "multiplicity " means here?

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

    I believe that multiplicity is the exponent value.

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

    Right? or am i mistaken.

  11. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes that is right

  12. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so if \(r\) is a zero with multiplicity \(n\) then one factor is \((x-r)^n\)

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

    Ok, that makes more sense. I don't know why I was so confused. Thank you!

  14. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.