If there are only three zeroes, we seem to have a cubic equation.
The factors are x-(-1)=x+1, x-1, and x-2. Multiply them together:
(x+1)(x-1)(x-2)=(x²-1)(x-2)=x³-2x²-x+2=0.
This is the most basic equation. Other zeroes could be complex.
For example, (x²+1)(x³-2x²-x+2)=x⁵-2x⁴-x³+2x²+x³-2x²-x+2=
x⁵-2x⁴-x+2=0. This has the same zeroes, but there are two complex zeroes as well. On a graph you would only see the zeroes you’ve given.
The blue curve is the cubic and the red curve is the degree 5 equation. Both have the same zeroes as you can see where they intersect on the axes.