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April 27, 2024, 01:36:37 pm
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Obama

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Maths problem
« on: November 09, 2008, 02:32:12 pm »
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Hey im new

1)Let f(x) be a monic polynomial* with integer coefficients with deg f(x) > 1. Prove that if the sum of all coefficients and the product of all the complex zeros (counting multiplicity) are both odd then the polynomial has not integer zeros.

*)Leading term is 1.
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Roflmao

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Re: Maths problem
« Reply #1 on: November 09, 2008, 02:36:27 pm »
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f(x) = (x-1)(x-5) =x3 - 9x2 + 23x - 15


The sum of the zeros is 9, the product of the zeros is 15, and all three zeros are integers.
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Flaming_Arrow

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Re: Maths problem
« Reply #2 on: November 09, 2008, 02:38:36 pm »
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Quote from: Roflmao on November 09, 2008, 02:36:27 pm
f(x) = (x-1)(x-5) =x3 - 9x2 + 23x - 15


The sum of the zeros is 9, the product of the zeros is 15, and all three zeros are integers.

Hi Ahmad?
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Roflmao

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Re: Maths problem
« Reply #3 on: November 09, 2008, 02:39:54 pm »
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Nah its me khalid :) Ahmad has his own account.
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Collin Li

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Re: Maths problem
« Reply #4 on: November 09, 2008, 02:40:04 pm »
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Moved to the general Mathematics board. In the future, please be more considerate to Maths Methods students, who have their exam either tomorrow or the day after, and may panic about material they have never heard of.
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bucket

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Re: Maths problem
« Reply #5 on: November 09, 2008, 02:50:56 pm »
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wtf khalid. not this again.

-
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Monash University
Science/Engineering (Maths, Physics and Electrical Engineering)

Collin Li

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Re: Maths problem
« Reply #6 on: November 09, 2008, 02:51:05 pm »
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Also, the hostname on Obama is jupiter.tmzproxy3.com and Roflmao's post comes 4 minutes after. Why do you enjoy answering your own questions?
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vce08

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Re: Maths problem
« Reply #7 on: November 09, 2008, 02:52:54 pm »
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He likes being smart.
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Roflmao

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Re: Maths problem
« Reply #8 on: November 09, 2008, 03:12:49 pm »
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Quote from: vce08 on November 09, 2008, 02:52:54 pm
He likes being smart.
Heheh i am smart but i abuse it
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humph

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Re: Maths problem
« Reply #9 on: November 09, 2008, 03:13:29 pm »
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VCE 2006
PhB (Hons) (Sc), ANU, 2007-2010
MPhil, ANU, 2011-2012
PhD, Princeton, 2012-2017
Research Associate, University College London, 2017-2020
Assistant Professor, University of Virginia, 2020-

Feel free to ask me about (advanced) mathematics.

Flaming_Arrow

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Re: Maths problem
« Reply #10 on: November 09, 2008, 03:59:59 pm »
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