GCD of polynomials?

1. Nov 21, 2008

tgt

Would the GCD of x^2+x+c and (x-a)^2+(x-a)+c always be 1?

2. Nov 21, 2008

tiny-tim

Hi tgt!

Hint: if the roots of the first one are p and q, what are the roots of the second one?

3. Nov 21, 2008

tgt

So it seems that two polynomials have nonzero GCD when there is at leaste one root shared between the two. So any two polynomials of the form a(x-t)^2+b(x-t)+c and ax^2+bx+c must have GCD 1 since they wouldn't have any roots shared between them.

4. Nov 22, 2008

tiny-tim

What about x2 + 3x + 2 = 0 and (x + 1)2 + 3(x + 1) + 2 = 0?

5. Nov 22, 2008

tgt

ok, I wasn't thinkng clearly at the time.