Question

Write the simplest polynomial function with zeros 4+i and sqrt of 2? help?!

Answer 1

x = 4+i is one root
x - 4 = i
square both sides:
(x-4)^2 = i^2
x^2 - 8x + 16 = -1
x^2 - 8x + 17 = 0

x = sqrt(2)
(x - sqrt(2)) is a factor.

Assuming irrational coefficients are okay, just multiply (x-sqrt(2)) and (x^2 - 8x + 17) and simplify.