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 March 21st, 2008, 11:48 AM #1 Newbie   Joined: Feb 2008 Posts: 8 Thanks: 0 Looks like a polynomial....but it isn't 8x^3-19x^(3/2)-27=0 , and x is an element of the complex numbers Please someone help me with this question. If it's not a polynomial then what is it? How many roots does it have, and what are they? March 21st, 2008, 02:03 PM #2 Member   Joined: Feb 2008 Posts: 89 Thanks: 0 [color=darkblue]Hi: By definition, the terms of a polynmial are of the form cx^n, where c is a real number and n is a whole number (i.e., a non-negative integer). Accordingly, 8x^3 - 19x^(3/2) - 27 is not a polynomial. That said, we can solve the given equation nonetheless. Begin with the substitution u = x^(3/2). Since x^3 = [x^(3/2)]^2 = u^2, the equation becomes, 8u^2 - 19u - 27 = 0, which factors as (8u-27)(u+1)=0 ==> u = 27/8 or u = -1. I leave it up to you to re-substitute x^(3/2) into these equations for u, and solve for x. Regards, Rich B.[/color] rmath4u2@aol.com March 26th, 2008, 02:39 AM #3 Newbie   Joined: Feb 2008 Posts: 8 Thanks: 0 But how do you know when to stop? I don't know the number of roots it has, that's the problem. Because it's not a polynomial I can't say it only contains 3 roots in the complex world, it probably contains more, but how many more? March 26th, 2008, 09:40 AM #4 Member   Joined: Feb 2008 Posts: 89 Thanks: 0 [color=darkblue]Hi Julien: Thanks for your input. So, do we have no way of knowing how many roots such a function has? Rich B.[/color] rmath4u2@aol.com March 26th, 2008, 10:57 AM #5 Global Moderator   Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms I would expect 6 roots, three from each of the u-values. You're taking cube roots, which should have three complex solutions. Tags polynomialbut Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post king.oslo Algebra 6 August 27th, 2013 06:11 AM alexmath Algebra 5 November 3rd, 2012 06:40 PM condemath Algebra 3 September 20th, 2011 08:34 PM unlimited Algebra 3 April 2nd, 2011 10:10 PM xcxc9 Linear Algebra 2 July 18th, 2010 04:18 PM

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