Step-by-step explanation:
the "number of zeros" means all values of x for which the expression delivers 0 as result.
so,
x⁴ + x + 2 = 0
now, any polynomial with n being the highest exponent of the variable has exactly n zeros.
some might be identical, some might be complex/imaginary numbers, but there are always n zeros.
so, in our case, we have 4 zeros.
FYI
in this case we have actually 4 complex numbers as solution (rather complicated expressions, so I skip the details).