Find a polynomial of degree 2 with real number coefficients and zero 3-2i

Complex roots occur as conjugates so the other root is 3 + 2i

so we have the factored form

(x - (3 - 2i) (x - (3 + 2i)

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

= x^2 - 3x - 2ix - 3x + 9 + 6i + 2ix - 6i - 4i^2

= x^2 - 6x + 9 + 4

= x^2 - 6x + 13 Answer