The polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4
Factorizing polynomial functions
Given the polynomial function below
F(x)=x³-x² + 4x-4
Group
F(x)=(x³-x²) + (4x-4)
f(x) = x²(x-1)+4(x-1)
f(x) = (x²+4)(x-1)
If f(x) = 0
x²+4 = 0 and x -1. = 0
x² = -4 and x = 1
x = ±2i and -1
Hence polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4
Learn more on zeros of polynomial here: https://brainly.com/question/11724515
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