Search   Memberlist   Usergroups
 Page 1 of 1 [7 Posts]
Author Message
jacob navia
science forum beginner

Joined: 06 Jul 2005
Posts: 30

Posted: Sun Jul 16, 2006 5:51 pm    Post subject: Solving a polynomial

Given
x^9 - 1000092x^8 + 92003682x^7 - 3682083720x^6 + 83721182769x^5 -
1182779630508x^4 + 10630567354028x^3 - 59354216204400x^2 +
1.882046594592e14x - 2.594592e14 = 0

Using a solver using the Jenkings-Traub method (from the page of
I obtain
[ 1] Re: 8.0000000000000067400 Im: 0.0000000000000000000
[ 2] Re: 8.9999999999999727200 Im: 0.0000000000000000000
[ 3] Re: 9.9999999999999436200 Im: 0.0000000000000000000
[ 4] Re: 11.0000000000004890000 Im: 0.0000000000000000000
[ 5] Re: 11.9999999999989139000 Im: 0.0000000000000000000
[ 6] Re: 13.0000000000011665000 Im: 0.0000000000000000000
[ 7] Re: 13.9999999999993683000 Im: 0.0000000000000000000
[ 8] Re: 15.0000000000001392000 Im: 0.0000000000000000000
[ 9] Re: 999999.0000000000000000000 Im: 0.0000000000000000000

Using mathematica online at http://www.mathe-online.at I obtain
a result I can't figure out at all.
13 2
{{x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 +

13 3 12 4 10 5
 Quote: 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 -

9 6 7 7 6 8 9
 Quote: 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 1]},

13 2
 Quote: {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 +

13 3 12 4 10 5
 Quote: 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 -

9 6 7 7 6 8 9
 Quote: 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 2]},

13 2
 Quote: {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 +

13 3 12 4 10 5
 Quote: 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 -

9 6 7 7 6 8 9
 Quote: 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 3]},

13 2
 Quote: {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 +

13 3 12 4 10 5
 Quote: 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 -

9 6 7 7 6 8 9
 Quote: 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 4]},

13 2
 Quote: {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 +

13 3 12 4 10 5
 Quote: 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 -

9 6 7 7 6 8 9
 Quote: 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 5]},

13 2
 Quote: {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 +

13 3 12 4 10 5
 Quote: 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 -

9 6 7 7 6 8 9
 Quote: 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 6]},

13 2
 Quote: {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 +

13 3 12 4 10 5
 Quote: 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 -

9 6 7 7 6 8 9
 Quote: 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 7]},

13 2
 Quote: {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 +

13 3 12 4 10 5
 Quote: 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 -

9 6 7 7 6 8 9
 Quote: 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 8]},

13 2
 Quote: {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 +

13 3 12 4 10 5
 Quote: 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 -

9 6 7 7 6 8 9
 Quote: 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 9]}}

Anyone there tell me what I am doing wrong?

jacob
Axel Vogt

Joined: 03 May 2005
Posts: 93

 Posted: Sun Jul 16, 2006 6:34 pm    Post subject: Re: Solving a polynomial May be it is like in Maple, you have to force Root to spit out its solutions (as a CAS may work symbolical with the roots). Here is it is Maple: restart; Digits:=14: eq:= x^9 - 1000092*x^8 + 92003682*x^7 - 3682083720*x^6 + 83721182769*x^5 - 1182779630508*x^4 + 10630567354028*x^3 - 59354216204400*x^2 + 1.882046594592e14*x - 2.594592e14: R:='RootOf(eq)'; allvalues(R); R := RootOf(eq) 7 8., 9., 10., 11., 12., 13., 14., 15., 0.1000000 10
Jean-Marc Gulliet
science forum beginner

Joined: 28 May 2005
Posts: 38

Posted: Sun Jul 16, 2006 9:34 pm    Post subject: Re: Solving a polynomial

jacob navia wrote:
 Quote: Given x^9 - 1000092x^8 + 92003682x^7 - 3682083720x^6 + 83721182769x^5 - 1182779630508x^4 + 10630567354028x^3 - 59354216204400x^2 + 1.882046594592e14x - 2.594592e14 = 0 Using a solver using the Jenkings-Traub method (from the page of the math wizard C. Bond: http://www.crbond.com/download/misc/rpoly.cpp) I obtain [ 1] Re: 8.0000000000000067400 Im: 0.0000000000000000000 [ 2] Re: 8.9999999999999727200 Im: 0.0000000000000000000 [ 3] Re: 9.9999999999999436200 Im: 0.0000000000000000000 [ 4] Re: 11.0000000000004890000 Im: 0.0000000000000000000 [ 5] Re: 11.9999999999989139000 Im: 0.0000000000000000000 [ 6] Re: 13.0000000000011665000 Im: 0.0000000000000000000 [ 7] Re: 13.9999999999993683000 Im: 0.0000000000000000000 [ 8] Re: 15.0000000000001392000 Im: 0.0000000000000000000 [ 9] Re: 999999.0000000000000000000 Im: 0.0000000000000000000 Using mathematica online at http://www.mathe-online.at I obtain a result I can't figure out at all. 13 2 {{x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 1]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 2]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 3]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 4]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 5]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 6]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 7]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 8]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 9]}} Anyone there tell me what I am doing wrong? Thanks in advance jacob

Hi Jacob,

I do not think you have done anything wrong since the solution returned
by Mathematica is valid: Root objects are an exact symbolic
representation of a solution (same thing as in Maple, see Axel Vogt
email), which are returned by the built-in function Solve.

However, the results returned by Mathematica 5.2 for Windows (on my
computer) are the correct numerical values. I tried to check the online
version you used but to no avail: I had been repeatedly unable to
connect to the server (time out error) before I gave up and wrote this
email.

Solve[x^9 - 1000092*x^8 + 92003682*x^7 - 3682083720*x^6 +
83721182769*x^5 - 1182779630508*x^4 + 10630567354028*x^3 -
59354216204400*x^2 + 1.882046594592*10^14*x - 2.594592*10^14 == 0, x]

returns

{{x -> 7.999999999973662}, {x -> 9.000000000257524}, {x ->
9.999999998875227}, {x -> 11.000000002819503}, {x -> 11.99999999566689},
{x -> 13.000000004035554}, {x -> 13.999999997912402}, {x ->
15.000000000459247}, {x -> 1.*^6}})

To get more info on Root objects in Mathematica, see
http://documents.wolfram.com/mathematica/functions/Root

HTH,
Jean-Marc
rjf
science forum beginner

Joined: 05 May 2006
Posts: 5

Posted: Sun Jul 16, 2006 10:16 pm    Post subject: Re: Solving a polynomial

For a start, your polynomial is in several more variables than you
intended.

1.882e14x is 1.882 * e14x, so you have introduced an extra
variable e14x.

Presumably you mean to write this: 1.882*10^(14)*x.

Also you probably should use NSolve rather than Solve.

There is a certain burden in using programs like Mathematica. You have
to provide the
input in the syntax expected by the program.

RJF

Jean-Marc Gulliet wrote:
 Quote: jacob navia wrote: Given x^9 - 1000092x^8 + 92003682x^7 - 3682083720x^6 + 83721182769x^5 - 1182779630508x^4 + 10630567354028x^3 - 59354216204400x^2 + 1.882046594592e14x - 2.594592e14 = 0 Using a solver using the Jenkings-Traub method (from the page of the math wizard C. Bond: http://www.crbond.com/download/misc/rpoly.cpp) I obtain [ 1] Re: 8.0000000000000067400 Im: 0.0000000000000000000 [ 2] Re: 8.9999999999999727200 Im: 0.0000000000000000000 [ 3] Re: 9.9999999999999436200 Im: 0.0000000000000000000 [ 4] Re: 11.0000000000004890000 Im: 0.0000000000000000000 [ 5] Re: 11.9999999999989139000 Im: 0.0000000000000000000 [ 6] Re: 13.0000000000011665000 Im: 0.0000000000000000000 [ 7] Re: 13.9999999999993683000 Im: 0.0000000000000000000 [ 8] Re: 15.0000000000001392000 Im: 0.0000000000000000000 [ 9] Re: 999999.0000000000000000000 Im: 0.0000000000000000000 Using mathematica online at http://www.mathe-online.at I obtain a result I can't figure out at all. 13 2 {{x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 1]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 2]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 3]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 4]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 5]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 6]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 7]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 8]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 9]}} Anyone there tell me what I am doing wrong? Thanks in advance jacob Hi Jacob, I do not think you have done anything wrong since the solution returned by Mathematica is valid: Root objects are an exact symbolic representation of a solution (same thing as in Maple, see Axel Vogt email), which are returned by the built-in function Solve. However, the results returned by Mathematica 5.2 for Windows (on my computer) are the correct numerical values. I tried to check the online version you used but to no avail: I had been repeatedly unable to connect to the server (time out error) before I gave up and wrote this email. Solve[x^9 - 1000092*x^8 + 92003682*x^7 - 3682083720*x^6 + 83721182769*x^5 - 1182779630508*x^4 + 10630567354028*x^3 - 59354216204400*x^2 + 1.882046594592*10^14*x - 2.594592*10^14 == 0, x] returns {{x -> 7.999999999973662}, {x -> 9.000000000257524}, {x - 9.999999998875227}, {x -> 11.000000002819503}, {x -> 11.99999999566689}, {x -> 13.000000004035554}, {x -> 13.999999997912402}, {x - 15.000000000459247}, {x -> 1.*^6}}) To get more info on Root objects in Mathematica, see http://documents.wolfram.com/mathematica/functions/Root HTH, Jean-Marc
jacob navia
science forum beginner

Joined: 06 Jul 2005
Posts: 30

Posted: Sun Jul 16, 2006 11:29 pm    Post subject: Re: Solving a polynomial

rjf a écrit :
 Quote: For a start, your polynomial is in several more variables than you intended. 1.882e14x is 1.882 * e14x, so you have introduced an extra variable e14x. Presumably you mean to write this: 1.882*10^(14)*x.

GASP!

Err....

Thanks and excuse me but by the life of me I would never thought about
THIS problem :-)

I mean the notation 1.234e12 is SO UNIVERSAL spanning fortran, C, C++
probably C# Java lisp and so many others that I just took it for
granted.

jacob navia
science forum beginner

Joined: 06 Jul 2005
Posts: 30

Posted: Sun Jul 16, 2006 11:30 pm    Post subject: Re: Solving a polynomial

Jean-Marc Gulliet a Ã©crit :
 Quote: jacob navia wrote: Given x^9 - 1000092x^8 + 92003682x^7 - 3682083720x^6 + 83721182769x^5 - 1182779630508x^4 + 10630567354028x^3 - 59354216204400x^2 + 1.882046594592e14x - 2.594592e14 = 0 Using a solver using the Jenkings-Traub method (from the page of the math wizard C. Bond: http://www.crbond.com/download/misc/rpoly.cpp) I obtain [ 1] Re: 8.0000000000000067400 Im: 0.0000000000000000000 [ 2] Re: 8.9999999999999727200 Im: 0.0000000000000000000 [ 3] Re: 9.9999999999999436200 Im: 0.0000000000000000000 [ 4] Re: 11.0000000000004890000 Im: 0.0000000000000000000 [ 5] Re: 11.9999999999989139000 Im: 0.0000000000000000000 [ 6] Re: 13.0000000000011665000 Im: 0.0000000000000000000 [ 7] Re: 13.9999999999993683000 Im: 0.0000000000000000000 [ 8] Re: 15.0000000000001392000 Im: 0.0000000000000000000 [ 9] Re: 999999.0000000000000000000 Im: 0.0000000000000000000 Using mathematica online at http://www.mathe-online.at I obtain a result I can't figure out at all. 13 2 {{x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 1]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 2]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 3]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 4]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 5]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 6]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 7]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 8]}, 13 2 {x -> Root[-2.59459 e14 + 1.88205 e14x - 5.93542 10 #1 + 13 3 12 4 10 5 1.06306 10 #1 - 1.18278 10 #1 + 8.37212 10 #1 - 9 6 7 7 6 8 9 3.68208 10 #1 + 9.20037 10 #1 - 1.00009 10 #1 + #1 & , 9]}} Anyone there tell me what I am doing wrong? Thanks in advance jacob Hi Jacob, I do not think you have done anything wrong since the solution returned by Mathematica is valid: Root objects are an exact symbolic representation of a solution (same thing as in Maple, see Axel Vogt email), which are returned by the built-in function Solve. However, the results returned by Mathematica 5.2 for Windows (on my computer) are the correct numerical values. I tried to check the online version you used but to no avail: I had been repeatedly unable to connect to the server (time out error) before I gave up and wrote this email. Solve[x^9 - 1000092*x^8 + 92003682*x^7 - 3682083720*x^6 + 83721182769*x^5 - 1182779630508*x^4 + 10630567354028*x^3 - 59354216204400*x^2 + 1.882046594592*10^14*x - 2.594592*10^14 == 0, x] ^^^^^^^^^^ ^^^^^^^

That was my mistake.

Thanks and excuse me for this blunder

jacob
Dana DeLouis
science forum beginner

Joined: 06 Mar 2006
Posts: 37

Posted: Mon Jul 17, 2006 12:57 pm    Post subject: Re: Solving a polynomial

 Quote: + 1.882046594592*10^14*x - 2.594592*10^14

As a side note with Mathematica, you can also enter the number as

1.882046594592*^14x - 2.594592*^14

I believe the idea is that Mathematica will not waste time (whatever that
means :>) ) actually multiplying these two numbers as in an equation (
xxx*10^14)

Just something different...

equ = x^9 - 1000092*x^8 + 92003682*x^7 -
3682083720*x^6 + 83721182769*x^5 -
1182779630508*x^4 + 10630567354028*x^3 -
59354216204400*x^2 + 1.882046594592*^14*x -
2.594592*^14 == 0;

equ2 = Rationalize[equ, 0];

Solve[equ2]

{{x -> 8}, {x -> 9}, {x -> 10}, {x -> 11},
{x -> 12}, {x -> 13}, {x -> 14}, {x -> 15},
{x -> 1000000}}
--
HTH. :>)
Dana DeLouis

"jacob navia" <jacob@jacob.remcomp.fr> wrote in message
news:44bacc21\$0\$851\$ba4acef3@news.orange.fr...
 Quote: Jean-Marc Gulliet a écrit : jacob navia wrote: Given x^9 - 1000092x^8 + 92003682x^7 - 3682083720x^6 + 83721182769x^5 - 1182779630508x^4 + 10630567354028x^3 - 59354216204400x^2 + 1.882046594592e14x - 2.594592e14 = 0 Using a solver using the Jenkings-Traub method (from the page of the math wizard C. Bond: http://www.crbond.com/download/misc/rpoly.cpp) I obtain [ 1] Re: 8.0000000000000067400 Im: 0.0000000000000000000 [ 2] Re: 8.9999999999999727200 Im: 0.0000000000000000000 [ 3] Re: 9.9999999999999436200 Im: 0.0000000000000000000 [ 4] Re: 11.0000000000004890000 Im: 0.0000000000000000000 [ 5] Re: 11.9999999999989139000 Im: 0.0000000000000000000 [ 6] Re: 13.0000000000011665000 Im: 0.0000000000000000000 [ 7] Re: 13.9999999999993683000 Im: 0.0000000000000000000 [ 8] Re: 15.0000000000001392000 Im: 0.0000000000000000000 [ 9] Re: 999999.0000000000000000000 Im: 0.0000000000000000000

<snip>
 Quote: Solve[x^9 - 1000092*x^8 + 92003682*x^7 - 3682083720*x^6 + 83721182769*x^5 - 1182779630508*x^4 + 10630567354028*x^3 - 59354216204400*x^2 + 1.882046594592*10^14*x - 2.594592*10^14 == 0, x] ^^^^^^^^^^ ^^^^^^^

 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
 Page 1 of 1 [7 Posts]
 The time now is Thu Dec 13, 2018 1:40 pm | All times are GMT
 Jump to: Select a forum-------------------Forum index|___Science and Technology    |___Math    |   |___Research    |   |___num-analysis    |   |___Symbolic    |   |___Combinatorics    |   |___Probability    |   |   |___Prediction    |   |       |   |___Undergraduate    |   |___Recreational    |       |___Physics    |   |___Research    |   |___New Theories    |   |___Acoustics    |   |___Electromagnetics    |   |___Strings    |   |___Particle    |   |___Fusion    |   |___Relativity    |       |___Chem    |   |___Analytical    |   |___Electrochem    |   |   |___Battery    |   |       |   |___Coatings    |       |___Engineering        |___Control        |___Mechanics        |___Chemical

 Topic Author Forum Replies Last Post Similar Topics Entire functions, polynomial bounds david petry Math 2 Thu Jul 20, 2006 11:09 pm inverting a cubic polynomial as a series pluton Math 6 Tue Jul 18, 2006 4:54 am Solving exponential inequality: a^x + b = c^x ??? Angelina.Paris@gmail.com1 Math 7 Mon Jul 17, 2006 3:51 am Polynomial solving jacob navia num-analysis 4 Sun Jul 16, 2006 6:12 pm Constructing a (GF(2^m)) polynomial from its roots using ... jaco.versfeld@gmail.com Math 2 Mon Jul 10, 2006 9:10 am