Question

Find all roots of f(x)=x³-7x²+20x+14 in ℤ and ℚ

Answer 1

What do you mean by "in Z and Q?"

Do you want the values of x for which f(x) = 0?
The only real root of f(x) = 0 is
-0.5748455821794285

There are two complex roots
3.7874227910897145 +/- 3.163826025580645 i

I used an online cubic solver.