Results 1 to 6 of 6

Math Help - positive roots?

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    25

    positive roots?

    Hi can someone help.

    Q. Determine whether these equations have positive roots

    i)\ s^3 + 6s^2 + 11s + 6 = 0
    ii)\ s^3 + s^2 - 8s - 12 = 0

    Cheers
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    676
    Thanks
    19
    Quote Originally Posted by anothernewbie View Post
    Hi can someone help.

    Q. Determine whether these equations have positive roots

    i)\ s^3 + 6s^2 + 11s + 6 = 0
    ii)\ s^3 + s^2 - 8s - 12 = 0

    Cheers
    The first equation has a root at -2, so by synthetic division you can write the (s+2)(-2s^2-8s-6)=0 You know how to solve quadratics right? Find the roots of -2s^2-8s-6=0.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2009
    Posts
    25
    thanks, i get (-3,-1), I am still a little confused about how you found the first one to have a root of -2?

    Cheers
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    1) If s>0 then s^3+6s^2+11s+6>0. Then the equation has no positive real root.

    2) s=3 is one of the roots.

    Then s^3+s^2-8s-12=(s-3)(s+2)^2=0

    The other two roots are equal with -2.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    676
    Thanks
    19
    Quote Originally Posted by anothernewbie View Post
    thanks, i get (-3,-1), I am still a little confused about how you found the first one to have a root of -2?

    Cheers
    I used calculus to guess the root. There's different ways you can find roots. If you find just one, you can find the others easily. There are a set of equations you can find here:

    Vičte's formulas - Wikipedia, the free encyclopedia

    Also, view this thread:

    http://www.mathhelpforum.com/math-he...tml#post381368
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Oct 2009
    Posts
    25
    Thanks very much mate that helps alot.

    R
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] +/- ve notation for roots, positive/negative, etc.
    Posted in the Algebra Forum
    Replies: 16
    Last Post: May 9th 2011, 10:57 AM
  2. Replies: 9
    Last Post: April 18th 2010, 12:28 AM
  3. Negative/positive Roots?
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 29th 2009, 11:29 AM
  4. Replies: 4
    Last Post: October 16th 2008, 03:46 AM
  5. Every Positive Number Has A Unique Positive Square Root
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: May 2nd 2008, 08:26 AM

Search Tags


/mathhelpforum @mathhelpforum