If a monic polynomial of degree n has n roots in Z, then..... (elementary algebra)

Question

If a monic polynomial of degree n has n roots in Z, then all it's coefficients are in Z.....State true or false and give a proof supporting your answer.

Answer 1

True. Consider the polynomial factorised into its roots: (x-a)(x-b)...(x-z) where a, b, z, etc. are all in Z, then the expansion of the product of the factors will contain the products, sums of products, of combinations of a, b, ...z. But these quantities are, by definition, contained in Z. The products and sums of products form the coefficients in the expansion, therefore the coefficients are all in Z.

Comments

So what is the final answer.... True or False....?? Also plz have a look at this question.... http://mathhomeworkanswers.org/215070/1-2-3-n-is-elementary-algebra

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I guess it's true coz it satisfies the condition but still I need to be sure on my side

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http://mathhomeworkanswers.org/215392/prove-that-if-a-and-b-are-sets-such-that-elementary-algebra Pls have a look at this as well

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I left a comment on this question. I did look at it but I failed to answer it successfully, so I deleted my answer.