Suppose that $a(x)f(x) +b(x)g(x) = 135$ where $a(x), b(x), f(x)$ and $g(x)$ are polynomials over $F$. Prove that $f(x)$ and $g(x)$ do not have any roots in common.
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2026-03-26 20:44:11.1774557851
Prove that $f(x)$ and $g(x)$ do not have any roots in common.
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Suppose there was a root in common $\alpha$ and plug it into your identity.