I need help with finding the polynomial with the lowest degree!

Question

Question:

-Find polynomial with the lowest degree:

-Zeros: 1, 3i,1+squareroot of 2, 1-i

Answer 1

Complex roots always come in conjugate pairs:

 

If 3i then -3i

If 1 - i then 1 + i

 

Since a ± appears in the quadratic formula

 

If 1 + √2, then 1 - √2

 

f(x) = (x - 3i)(x + 3i)(x - 1 - √2)(x + 1 + √2)(x - 1)

 

Answer 2

F(x)=(x-1)•(x-3i)

     •(x-(1+sqrt(2)))•(x-(1-i))