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 January 25th, 2010, 05:28 PM #1 Senior Member   Joined: Jan 2009 Posts: 345 Thanks: 3 Find the quadratic equation with integer coefficients in... The equation $x^2+x-2009=0$, has two non-zero roots m and n. Find the quadratic equation with integer coefficients in the form of $ax^2+bx+c=0$ whose roots are $\frac{1}{m}$ and $\frac{1}{n}$
January 26th, 2010, 01:29 PM   #2
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Re: Find the quadratic equation with integer coefficients in...

Quote:
 Originally Posted by alevis The equation $x^2+x-2009=0$, has two non-zero roots m and n. Find the quadratic equation with integer coefficients in the form of $ax^2+bx+c=0$ whose roots are $\frac{1}{m}$ and $\frac{1}{n}$
$1+x-2009x^2=0$

January 26th, 2010, 03:00 PM   #3
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Re: Find the quadratic equation with integer coefficients in...

Quote:
 Originally Posted by alevis The equation $x^2+x-2009=0$, has two non-zero roots m and n. Find the quadratic equation with integer coefficients in the form of $ax^2+bx+c=0$ whose roots are $\frac{1}{m}$ and $\frac{1}{n}$

Please explain how you arrived at that solution

 January 26th, 2010, 08:20 PM #4 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Find the quadratic equation with integer coefficients in... Expand (x-m)(x-n) and $(x-\frac1m)(x-\frac1n)$ and compare. What happens if you multiply the latter by mn?
January 27th, 2010, 12:42 PM   #5
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Re: Find the quadratic equation with integer coefficients in...

Quote:
Originally Posted by alevis
Quote:
 Originally Posted by alevis The equation $x^2+x-2009=0$, has two non-zero roots m and n. Find the quadratic equation with integer coefficients in the form of $ax^2+bx+c=0$ whose roots are $\frac{1}{m}$ and $\frac{1}{n}$

Please explain how you arrived at that solution
Replace x by 1/x.

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