Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

swissgirl

  • 2 years ago

How to find the complex roots of \(x^4+x^3+3x^2+2x+2 \)

  • This Question is Closed
  1. dumbcow
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you have to factor out any real roots easiest to graph the function to obtain any real roots

  2. swissgirl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    There are no real roots though

  3. swissgirl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its above the y axis

  4. experimentX
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    let (x^2+bx+1)(x^2+cx+2) = that expression and find the value of b and c

  5. dumbcow
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    ok then yeah what @experimentX said if two of the complex roots is in the form: \[x = a \pm bi\] then \[x-a = \pm bi\] \[(x-a)^{2} = -b^{2}\] \[x^{2}+ (-2a)x +(a^{2}+b^{2}) = 0\] anyway , my point is that a pair of complex roots come from a quadratic equation :|

  6. KingGeorge
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I imagine you could factor this by grouping and then use the quadratic formula again.

  7. swissgirl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i tried doing the method u taught me yesterday but it wldnt go

  8. KingGeorge
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\Large x^4+x^3+3x^2+2x+2 \\ \Large =x^4+2x^2+x^3+x^2+2(x+1)\\ \Large =x^4+2x^2+x^2(x+1)+2(x+1)\\ \Large =x^2(x^2+2)+(x^2+2)(x+1)\\ \Large =(x^2+2)(x^2+x+1)\]

  9. KingGeorge
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I think the trick is seeing to split up the \(3x^2\) as \(2x^2+x^2\).

  10. swissgirl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    omg y is it always sooooo simple and I can never see it lol

  11. swissgirl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanksssss guyssss for helping me :))))

  12. KingGeorge
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    You're welcome.

  13. 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.