Math Help Forum - View Single Post - Algebra with pq-formula

liljeros · #3 May 22nd, 2008, 11:32 AM

Quote:

Originally Posted by masters

If $x_1=a$ is a root, then $x-a$ is a factor.

If $x_2=b$ is a root, then $x-b$ is a factor.

Therefore,

$(x-a)(x-b)=x(x-b)-a(x-b)=x^2-bx-ax+ab=0$

Simplifying (factoring out x in 2nd and 3rd terms):

$x^2-(a+b)x+ab=0$

"If $x_1=a$ is a root, then $x-a$ is a factor.

If $x_2=b$ is a root, then $x-b$ is a factor."

How come it is like this? Is it a rule of some kind?