Answer:
C. f (x) = x^3-3x^2-4x-2
Step-by-step explanation:
we know that
The conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial
In this problem we have that
The polynomial has roots 1 and (1+i)
so
by the conjugate root theorem
(1-i) is also a root of the polynomial
therefore
The lowest degree of the polynomial is 3
so
Remember that
The leading coefficient is 1
so
a=1