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Math Help - Finding the remaining zeros of each polynomial function

  1. #1
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    Red face Finding the remaining zeros of each polynomial function

    Use the given zero to find the remaining zero's of each polynomial function.


    P(x)= x^3+3x^2+x+3; -i



    I'm pretty lost with this stuff. I've been watching Patrick's videos trying to remember my high school days but wow it's been a while hehe.

    It looks like Conjugate Pair Theorem would be the way to solve. If I figure it out I'll post my solution.

    If you guys could give me some direction to help me get back into the game that would be AWESOME!!

    Thanks a TON
    Last edited by RBlax; June 4th 2010 at 11:03 AM.
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  2. #2
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    Quote Originally Posted by RBlax View Post
    Use the given zero to find the remaining zero's of each polynomial function.


    P(x)= x^3+3x^2+x+3; -i



    I'm pretty lost with this stuff. I've been watching Patrick's videos trying to remember my high school days but wow it's been a while hehe.

    If you guys could give me some direction to help me get back into the game that would be AWESOME!!

    Thanks a TON
    1. Since there are only real coefficients in the term of the function there must exist a 2nd solution x = +i. Thus (x^2+1) must be a factor in the term:

    2. P(x)= x^3+3x^2+x+3 = x^2(x+3) + (x+3) = (x+3)(x^2+1)

    3. A product equals zero if one factor equals zero. Use this property to determine the last missing zero of P.
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  3. #3
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    Hello, RBlax!

    Use the given zero to find the remaining zeros.

    . . P(x)\:=\: x^3+3x^2+x+3.\quad x = -i

    Since x = -i is a zero of P(x), then x = +i is also a zero.
    . .
    (Complex roots always appear in conjugate pairs.)

    Then: . [x - (-i)]\text{ and }[x - (+i)] are factors of P(x).

    . . That is: . (x + i)(x - i) \:=\:x^2+1 is a factor of P(x).


    Dividing, we find that: . P(x) \:=\:(x^2+1)(x+3)


    Therefore, the zeros of P(x) are: . i,\:-i,\:-3



    Edit: Too slow . . . again!
    .
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  4. #4
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    This isn't using the The Conjugate Pair Theorem though right?

    I think what they are wanting me to do looks something like...

    P(x)= x^3+3x^2+x+3; -i

    then use synthetic division (which I begin to become lost)

    Edit: I'm slow too haha

    But thanks a ton for the help.
    Last edited by RBlax; June 4th 2010 at 01:46 PM.
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