Final answer:
To determine if 1 - 2i is a zero of the given polynomial f(x), substitute it into the polynomial and simplify the expression.
Step-by-step explanation:
The given polynomial is:
f(x) = x^4 - 2x^3 - 1x^2 + 12x - 30
The zero given is: 1 - 2i
To determine if 1 - 2i is a zero of the polynomial, we can substitute it into the polynomial and see if it equals zero. If it does, then 1 - 2i is a zero.
Let's substitute 1 - 2i into the polynomial:
f(1 - 2i) = (1 - 2i)^4 - 2(1 - 2i)^3 - 1(1 - 2i)^2 + 12(1 - 2i) - 30
Simplifying this expression will help us determine if 1 - 2i is a zero of the polynomial.