I'm pretty sure that I am meant to use the evaluation map, but I'm confused about how to write a homomorphism that doesn't have a kernel of $(x-c)$ where $(x-c)^2$ is $x^2 +\bar ax +\bar 1$
2026-03-25 16:08:24.1774454904
Prove that if $x^2 +\bar ax +\bar 1$ has a double root, then $(\mathbb Z/5)[x]/I$ $\cong$ $(\mathbb Z/5)[x]/(x^2)$ where I = $x^2 +\bar ax +\bar 1$
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Hint: Consider $(\mathbb Z/5)[x]/(x^2) \to (\mathbb Z/5)[x]/I$ induced by $x \bmod x^2 \mapsto x-c \bmod I$.