Results 1 to 2 of 2

Math Help - problems of Roots of polynomials

  1. #1
    kin
    kin is offline
    Junior Member
    Joined
    Sep 2009
    Posts
    53

    problems of Roots of polynomials

    M^3 - M -1 =0

    how to solve for M...?
    i take approximation for M=1.33, am i right?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Oct 2009
    Posts
    68
    Quote Originally Posted by kin View Post
    M^3 - M -1 =0

    how to solve for M...?
    i take approximation for M=1.33, am i right?
    There are many numerical methods you can use for finding approximations to the real root of the equation. Use the intermediate-value theorem to narrow it down first; in this case, the real root is between 1 and 1.5. Then you can apply, for example, Newton’s method to the polynomial.

    For an analytic solution, you can use Cardano’s method, which in this case yields an exact solution of \sqrt[3]{\frac{1+\sqrt{\frac{23}{27}}}2}+\sqrt[3]{\frac{1-\sqrt{\frac{23}{27}}}2} for the real root (which is approximately 1.3247).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: April 7th 2011, 12:38 PM
  2. Roots of polynomials
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 4th 2010, 10:27 AM
  3. Polynomials with many roots
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: August 1st 2008, 02:10 PM
  4. roots of polynomials
    Posted in the Algebra Forum
    Replies: 4
    Last Post: May 26th 2008, 03:53 PM
  5. Roots of a sum of polynomials
    Posted in the Algebra Forum
    Replies: 0
    Last Post: March 24th 2008, 02:31 PM

Search Tags


/mathhelpforum @mathhelpforum