Re: Real roots of polynomials

• To: mathgroup at smc.vnet.net
• Subject: [mg24724] Re: Real roots of polynomials
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Wed, 9 Aug 2000 02:31:23 -0400 (EDT)
• References: <8mdl69\$5hc@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Jack,

How abour using InequalitySolve?

<<Algebra`InequalitySolve`

poly = Expand[x (x^2 - 2) (x^2 - 3)(x^8 - 3.)]//N

3       5       9       11    13
-18. x + 15. x  - 3. x  + 6. x  - 5. x   + x

InequalitySolve[poly == 0, x]

x == -1.73205 || x == -1.41421 || x == -1.1472 || x == 0. || x == 1.1472 ||
x == 1.41421 ||

x == 1.73205

Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Jack Goldberg" <jackgold at math.lsa.umich.edu> wrote in message
news:8mdl69\$5hc at smc.vnet.net...
> Hi,
>
> Suppose  Pn[x]  is a polynomial of degree n in x.  Its coefficients
> are real.
>
> Question:  What is a good way of determining the real roots of Pn
> and their multiplicities?
>
> Use NSolve and "cast out" the complex roots and Chop any
> roots with a "too" small imaginary part (in case NSolve
> inserts spurious imaginary parts).
> In cases where  n  is large and the number of real roots is small
> compared to  n, one can imagine that better methods exist.  I have
> searched MathSource with no real (pun intended) progress.  Possibly
> this is more a math question than a Mathematica question.
>
> Help is appreciated.
>
> Jack
>
>
>

```

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