Construct a polynomial with given roots
J, 8 bytes
A series of verbs:
|.p.1;~.

Call it like this:
   |.p.1;~. 1 2
1 _3 2

J has a built-in verb p. (Roots). It converts between polynomials like 2 _3 1 (reverse order from the problem) and a multiplier/root pair like (1; 1 2).
From right-to-left, ~. takes the unique elements, 1; pairs the list with 1, meaning we want the smallest integer polynomial, p. does the actual work, and |. reverses the resulting list.