Answer:
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
