tgt
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Would the GCD of x^2+x+c and (x-a)^2+(x-a)+c always be 1?
GCD of Polynomials: Is 1 Always the Solution?
- Context: Undergrad
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tgt said:
Hi tgt!
Hint: if the roots of the first one are p and q, what are the roots of the second one?
tgt
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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.
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tgt said:
What about x2 + 3x + 2 = 0 and (x + 1)2 + 3(x + 1) + 2 = 0?
tgt
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tiny-tim said:What about x2 + 3x + 2 = 0 and (x + 1)2 + 3(x + 1) + 2 = 0?
ok, I wasn't thinkng clearly at the time.