Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

DeadShot

  • one year ago

How would I set this up to solve it? Find the polynomial function with roots 1, 7, and -3 of multiplicity 2.

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

    All the roots of multiplicity \(2\)?

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

    And here's your example: If you want a polynomial with root \(2\) of multiplicity \(3\),\[(x - 2)^3\]

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

    so, root -3 of multiplicity 2 would be \[(x - (-3))^2\] right?

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

    That is correct :-)

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

    So is it only \(-3\) with multiplicity \(2\)?

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

    I have no idea, the question on my homework says "Find the polynomial function with roots 1, 7, and -3 of multiplicity 2.", the teacher didn't say anything else about it.

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

    so, \[(x-1) (x-7) (x-(-3))^2\] is the correct way to set it up?

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

    Yes, that's correct! But if we have all those with multiplicity \(2\),\[(x - 1)^2(x - 7)^2(x + 3)^2\]

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

    ok, so I'll do all of them with multiplicity of two. \[(x-1)^2 (x-7)^2 (x-(-3))^2\] and then solve it.

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

    I dunno, it's your choice. It can be either.

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

    So, it becomes \[(x^2 + 1) (x^2 + 49) (x^2 + 9)\] right?

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

    I think it's just \(-3\) with multiplicity of \(2\).

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

    They don't usually give such hard problems.

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

    oh, so then it's \[(x-1) (x-7) (x^2 + 9)\] right?

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

    Hey wait, don't we have the same pics?

  16. ash2326
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It should be \[(x-1) (x-7) (x + 3)^2\]

  17. ash2326
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[(x+3)^2\ne x^2+9\] \[(x+3)^2=x^2+2\times 3\times x+3^2\]

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

    Why is OpenStudy so slow right now?

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

    so, then it's \[(x-1) (x-7) (x^2 + 6x + 9)\] ?

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

    thats correct, but i think you need to multiply them out for final answer, and bring it in the form, ax^4+bx^3+cx^2+dx+e

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

    Yes.

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

    so then the answer is \[(x^4 + 6x^3 - x^3 - 7x^3- x^2 - 7x^2 -6x - 42x - 9 - 63) \] simplified, it is \[(x^4 - 2x^3 - 8x^2 - 48x - 72)\] right?

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

    Yup

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

    ok, thanks!

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

    • Attachments:

Ask your own question

Ask a Question
Find 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
  • 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.