Question #0134b

1 Answer
Jim H
Oct 17, 2017

Please see below.

Explanation:

Given that the zeros of the polynomial are #2# and #1-i#, we know that the factors must be #x-2# and #x-(1-i)#.

Since we are asked for "a" polynomial, let's assume that we are permitted to answer with a polynomial of degree #2# (the minimum degree to have two zeros.)

Start with
#P(x) = (x-2)(x-(1-i))#.

To get standard form, expand.

#P(x) = x^2-(1-i)x-2x+2(1-i)#

# = x^2-x+ix-2x+2-2i)#

# = x^2+(-3+i)x+(2-2i)#

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