[SOLVED] Show that r|b

**Deepu** · January 21st 2010, 03:47 PM

if r belongs integer and r is a non zerosolution of x^2+ax+b=0 (where a,b belongs to integers), prove that r|b.

**Jhevon** · January 21st 2010, 03:56 PM

Originally Posted by Deepu

if r belongs integer and r is a non zerosolution of x^2+ax+b=0 (where a,b belongs to integers), prove that r|b.

We are told that $r^2 + ar + b = 0$

$\Rightarrow r^2 + ar = -b$

$\Rightarrow r(r + a) = -b$

Now what can you say?

Spoiler:

**Deepu** · January 21st 2010, 04:17 PM

Originally Posted by Jhevon

We are told that $r^2 + ar + b = 0$

$\Rightarrow r^2 + ar = -b$

$\Rightarrow r(r + a) = -b$

Now what can you say?

Spoiler:

Thank you..

**Jhevon** · January 21st 2010, 04:20 PM

Originally Posted by Deepu

Thank you..

the conclusion follows even more immediately if you recall that $m|n \Longleftrightarrow n = mk \text{ for some }k \in \mathbb{Z}$

Thread: [SOLVED] Show that r|b