PLEASE EXPLAIN This is a college algebra problemThe answer i

PLEASE EXPLAIN. This is a college algebra problem.The answer is shown. Please explain how to arrive at this answer.

2. Let f be a fourth degree polynomial with real coefficients. Assume f has a repeated root at x 1 and another root at x 2i. Which of the following polynomials could be f?

Solution

f has all real coefficients that means if there is any complex root, there would also be the conjugate of it as root of the polynomial so the other root must be x =-2i

And since f is a 4th degree polynomial it will have 4 roots.

SO our roots are x = 1 , 1 ( since they are repeated)

and x = 2i and -2i

So the polynomial be (x-1)^2(x-2i)(x-(-2i))

or (x-1)^2(x-2i)(x+2i)

Hence option B is correct.