Question

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.



1) -2, -1, 1

2) i, 4

3) i, 2 - √3

4) 1, 4, 1 + √2

Answer 1

if the function has a zero at 3i , it must have also a zero at -3i
if the function has a zero at 2-i , it must have also a zero at 2+i

f(x) = (x - 3i) ( x+3i) ( x-2+i) ( x-2-i)
f(x) = (x² +9) ( x² -4x+5)