Suppose ƒ(x) = (x − a)(x − b)(x − c)^2. Which of the following are possible values of a,b, and c (see description)?

Question

A) a = 2 + i, b = 3i, and c = 4

B) a = 2 + i, b = 2 − i, and c = 3

C) a = 2 − 3i, b = 3, and c = 2 + 3i

D) a = √ 2 , b = √ 3 , and c = 5i

E) a = √ −2 , b = √ −3 , and c = 5

Multiple choice answers.

Answer 1

Assuming that a, b, and c are real numbers, complex roots must occur in conjugate pairs (that is, if x + yi is a root, then so is x - yi).

So, the answer must be choice B.