Answer:
D
Step-by-step explanation:
Given the roots of a polynomial, say x = a, x = b, x = c, then
(x - a), (x - b) and (x - c) are the factors and the polynomial is the product of the factors.
Note complex roots occur in conjugate pairs, thus
x = i is a root ⇒ x = - i is also a root
given roots x = 2, x = i, x = - i are roots, then
(x - 2), (x - i) and (x + i) are the factors and
f(x) = (x - 2)(x - i)(x + i)
= (x - 2)(x² - i²)
= (x - 2)(x² + 1)
= x³ + x - 2x² - 2
= x³ - 2x² + x - 2 → D
