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 May 9th, 2009, 09:16 AM #1 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond Polynomial Roots Can the expression p(x) - q(x) = 0 have infinitely many roots where p(x) and q(x) are both polynomials?
 May 9th, 2009, 09:44 AM #2 Senior Member   Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0 Re: Polynomial Roots $p(x)-q(x)$ is a polynomial of degree at most equal to the largest power of $x$ present in either $p$ or $q.$ Call this polynomial $r(x).$ So the expression $f(x)-q(x)=0$ is equivalent to $r(x)=0.$ Do you think there is any way this can this have infinite roots?
May 9th, 2009, 09:52 AM   #3
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Re: Polynomial Roots

Quote:
 Originally Posted by mattpi $p(x)-q(x)$ is a polynomial of degree at most equal to the largest power of $x$ present in either $p$ or $q.$ Call this polynomial $r(x).$ So the expression $f(x)-q(x)=0$ is equivalent to $r(x)=0.$ Do you think there is any way this can this have infinite roots?
No, definitely not. It is given as an answer in a book I am studying. Maybe I should find another book. Thanks.

May 9th, 2009, 10:03 AM   #4
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Re: Polynomial Roots

Quote:
Originally Posted by greg1313
Quote:
 Originally Posted by mattpi $p(x)-q(x)$ is a polynomial of degree at most equal to the largest power of $x$ present in either $p$ or $q.$ Call this polynomial $r(x).$ So the expression $f(x)-q(x)=0$ is equivalent to $r(x)=0.$ Do you think there is any way this can this have infinite roots?
No, definitely not. It is given as an answer in a book I am studying. Maybe I should find another book. Thanks.
What about if $p(x)=q(x)$ for all $x?$

 May 9th, 2009, 10:05 AM #5 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond Re: Polynomial Roots Yep. Got it now, thanks. (I guess I'll keep reading the book).

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