Results 1 to 4 of 4

Math Help - Use the given zero to find all the zeros of the function

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    54

    Use the given zero to find all the zeros of the function

    Use the given zero to find all the zeros of the function.
    f(x) = x^3 + x^2 + 9x + 9
    Given zero: r = 3i

    So, I think that I have to use synthetic division using 3i and -3i as roots?
    Is this right? If so, what is the next step?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member tedii's Avatar
    Joined
    Sep 2009
    From
    Milwaukee, Wisconsin
    Posts
    32
    Quote Originally Posted by tsmith View Post
    Use the given zero to find all the zeros of the function.
    f(x) = x^3 + x^2 + 9x + 9
    Given zero: r = 3i

    So, I think that I have to use synthetic division using 3i and -3i as roots?
    Is this right? If so, what is the next step?
    Since two of the zeros are 3i and -3i you can multiply their linear parts like so:

    (x-3i)(x+3i)=x^2+6i-6i-9(i^2)=
    x^2+9

    Now synthetically divide f(x) by x^2+9 and you should get your last zero solution.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by tsmith View Post
    Use the given zero to find all the zeros of the function.
    f(x) = x^3 + x^2 + 9x + 9
    Given zero: r = 3i

    So, I think that I have to use synthetic division using 3i and -3i as roots?
    Is this right? If so, what is the next step?
    The bold is correct. So you just need one more real root.
    (x^2+9) is is one factor.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member pacman's Avatar
    Joined
    Jul 2009
    Posts
    448
    factor: (x + 1)(x^2 + 9) = (x + 1)(x + 3i)(x - 3i),
    Attached Thumbnails Attached Thumbnails Use the given zero to find all the zeros of the function-j.gif   Use the given zero to find all the zeros of the function-ty.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find the zeros of this function
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 5th 2010, 10:17 PM
  2. Find the zeros of the function...
    Posted in the Algebra Forum
    Replies: 3
    Last Post: January 14th 2010, 03:50 PM
  3. Find all Zeros of the Function
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: October 16th 2009, 05:36 AM
  4. Find all the zeros of this function
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: September 21st 2009, 02:08 PM
  5. How to find the zeros of this function
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 17th 2009, 04:18 PM

Search Tags


/mathhelpforum @mathhelpforum