Find out the kernel of $\phi $?

Question

Given $\phi : \mathbb{Z}[x] \rightarrow \mathbb{R}$ given by $\phi(f(x)) := f( \sqrt 2)$ is a ring homomorphism. Find out the kernel of $\phi $

My attempt : kernel of $\phi $ is $x^2-2$

is its true ??

@jasmine Why are you duplicating questions? – Slup Oct 25 '19 at 12:26 — Slup, Oct 25 '19 at 12:26

score 1 · Accepted Answer · answered Oct 25 '19 at 11:36

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Hint: The kernel of a ring homomorphism is always an ideal.

answered Oct 25 '19 at 11:36

Ben Grossmann

That mean @Omnomnomnom .kernel of $\phi $ is $x^2-2$ – jasmine Oct 25 '19 at 14:01
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@jasmine but $x^2 - 2$ is not an ideal – Ben Grossmann Oct 25 '19 at 14:03
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@jasmine note for example that $x(x^2 - 2) = x^3 - 2x$ will also be an element of the kernel. – Ben Grossmann Oct 25 '19 at 14:05
thanks u , now got its @Omnomnomnom .....ur name is diificult to type – jasmine Oct 25 '19 at 14:17

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