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Answer:
f(x) = x³ +3x² -6x -18
Explanation:
In order for there to be a root of √6, there must be a factor of (x-√6). In order for there to be rational coefficients, there needs to be another factor of (x+√6) in the minimal polynomial. Then the minimal polynomial with the required roots is ...
f(x) = (x +3)(x -√6)(x +√6) = (x +3)(x² -6)
f(x) = x³ +3x² -6x -18