What is the equation of a quadratic function p with rational coefficients that has a zero of 3-i

p = x² - 6x + 10

Step-by-step explanation:

Complex roots come in conjugate pairs. So if 3-i is a root, then 3+i is also a root.

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

p = x² - (3+i) x - (3-i) x + (3-i) (3+i)

p = x² - 3x - ix - 3x + ix + (9 - i²)

p = x² - 6x + 10

You can check your answer using the quadratic formula.

x = [ - b ± √ (b² - 4ac) ] / 2a

x = [ 6 ± √ (36 - 40) ] / 2

x = (6 ± 2i) / 2

x = 3 ± i