I was tasked to find the polynomial equation of the lowest possible degree with real coefficients, which had the zeros 2, 11-i and -4+2i. I did that by finding the conjugate forms of the last two zeros and find the polynomial by multiplying the factors out:
Now for the second part, which I'm unsure about. I'm asked to find the polynomial q(z) of degree 6 with real coefficients, which has the exact same roots as p(z). Am I supposed to assume the root 2 is a double root? I could use some advice to lead me on the right path.