A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Find a third-degree polynomial with real coefficients and with zeros –3 and –4 + i.

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    one factor is \(x+3\) for sure the hard part is finding a quadrtic with zeros \(-4+i\) and\(-4-i\) there are three ways do to it one is hard one is easy one is real real easy you pick

  2. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol pick the hard way \(\color\magenta\heartsuit\)

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

    okay, lol.

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

    lets do the easy way first ] work backwards starting with \[x=-4+i\] then add 4 to both sides to get \[x+4=i\] square both sides (carefully) to get \[(x+4)^2=-1\] or \[x^2+8x+16=-1\]

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

    adding 1 gives you the quadratic as \[x^2+8x+17\]

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

    that is the easy wat

  7. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i guess that was easy...

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

    the real real easy way requires memorizing something namely, that if \(a+bi\) is a zero, the quadratic is \[x^2-2ax+(a^2+b^2)\] in your case \(a=-4,b=1\) so \[x^2-2(-4)x+(6^2+1^2)\] \[x^2+8x+17\]

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

    typo there, but you get the idea

  10. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah \[x^2-2(-4)x+((-4)^2+1^2)\]

  11. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lot easier than trying \[(x-(-4+i))(x-(-4-i))\]

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

    final job is to multiply \[(x+3)(x^2+8x+17)\]

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

    \[(x-(-4+i))(x-(-4-i))\] isn't hard either. It's in the form [(x+4)+i] * [(x+4)-i] which equals: (x+4)^2 + 1

  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.