Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ineedbiohelpandquick

  • 2 years ago

write (solve for) a polynomial with the following zeros a) 2 and -3i

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

    on of the polynomials is (x-2)(x^2+9)

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

    Can you explain how you got that answer please?:) thanks!

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

    if 2 is the zero of the polynomial then that polynomilal can be divided with (x-2) without rest....if 3i is the zero, then it's dividable with (x-3i)....you must know that 3i is the complex zero, and there is always one friend following him...it's -3i so this polynomial is dividable with (x-(-3i))=x+3i.....now you can multiply all the parenthesis and you get your polynomial....(x-2)(x-3i)(x+3i)....those last two give the difference of the squares...so you can write it as I did above....of course, you can multiply them also...:D

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

    You are amazing! Thanks :)

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

    if you'd like to see if you got this right, I can give you one example, and you can solve it here....check this one out....|dw:1330286335128:dw|

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

    Is that the final answer or do you have to multiply it out to get those zeros?

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

    whoops ignore what I just said. :)

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

    no no, it's OK...you have zeros given, and your task is to find polynomial which zeros are given for you....

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

    so like the (x-2) (x^2 +9) is ur final answer? sorry that is were i am confused haha

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

    you can leave it like that, but most professors would like to multiply...do you know how to do it"?

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

    Can you help explain that to me? if you have time:) .... ALSO my next question is 3 and 2+2i so the answer would just be... (3-x) and (x+2+2i) and (x-2+2i) ??

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

    well, OK lets start like this...do you know to multiply for example (x-2)(x+3)? it's some basic stuff you must know before you continue working with polynomials....multiply this so I can see...:D

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

    yes isn't it x^2+1x-6

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

    that's right....now we continue with this....for example if I tell you that one zero of the polynomial is some number, lets call it ''a'' that means that your polynomial is divisible with (x-a)...OK....now try to continue my next sentence: If -a is the zero of the polynomial, then your polynomial is divisible with...?

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

    (x+a)?

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

    great :D chocolate for you :D

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

    haha! yeah!

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

    so the final answer for the first one is: x^3-2x^2+9x-18?

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

    now, If I tell you this: Polynomial has zeros a and -a, so I can write that polynomial as (x-a)(x+a) and if I multiply those two I'll get x^2-a^2....now you anwer: Polynomial has zeros 1 and -6 then you can write you polynomial as ...??? and if you multiply those two you'll get ...????? :D try

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

    polynomial is (x-1) (x+6) and final answer is x^2+5x-6

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

    what is the polynomial of 2+2i though is it just (x-2+2i) and (x+2+2i)

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

    awesome!!! :D now the next step: If polynomial has zero i then it's divisible with (x-i)...now I told you earlier that i is ''complex zero'', and it never appears alone, it appears together with -i....so write that polynomial....and when you multiply use very important formula i^2=-1...try :D

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

    so i just multiply (factor) the (x-2+2i) and (x+2+2i) and (x-3) together haha

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

    be careful: if the given zero is 2+2i that means that your polynomial is divisible by x-(2+2i)...and it will appear with the ''friend'' 2-2i so its divisible also by (x-(2-2i)) so when you multiply those two, one thing is very important...every ''i'' in your polynomial must be cancelled....try to do it, so I can be sure you're not making any mistakes...:D

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

    (x-3) (8) i think i did something wrong

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

    i will show u what I did

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

    (x-3) (2+2i) (2-2i) (x-3) (4-4i+4i-4i^2) (x-3) (4+4) (x-3) (8)

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

    no no...you have to multiply (x-(2-2i))*((x-(2+2i))...try again, and be patient..:D

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

    ohh! so do you distribute the x to the 2-2i and 2+2i

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

    I didn't get that...just multiply and show me the procedure....

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

    I'm back in two minutes :D

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

    (x-3) (x-2+2i) (x-2-2i) is that right so far? :(

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

    yes, go,go,go...:D

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

    what do you do though when you multiply the x by -2i is it just -2ix?

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

    of course, continue...;D

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

    okay lets see... (x-3) (x^2-2x-2xi-2x+4-4i^2+2ix-4i-4i-4i^2) x^2-4x-4i^2+4+4-4i+4 x^2-4x+12-4i

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

    number ''i'' must be gone after mulitplication...try again, look out for signs, and of course use i^2=-1

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

    is the final answer x^2-4x+4

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

    thanks for all ur help:) btw

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

    no, try again.....the result you got now is (x-2)^2. That's polynomial with double zero x=2 so there's no 2+2i etc....you must try again....

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

    well now i got something crazy... x^4-10x+12 :((

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

    OK I'll do it...follow me carefuly: (x-2+2i)(x-2-2i)=x^2-2x-2xi-2x+4+4i+2xi-4i+4=x^2-4x+8 do you get it? you must be careful with doing this

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

    okay i get that part

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

    hahah...well that part is all!!! :D I hope I helped you :D

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

    Oh i was just combining it all wrong! thank you!!! :) yes you did!!

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

    you're welcome...when you have any troubles with math be free to contact me, I'll be glad to help you :D

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

    awesome for sure! I am pretty weak at math so I will for sure be contacting you!

  48. 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.