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

n zeroes means its degree is n. now, for an equation with 3 zeroes, write it as (x-a)(x-b)(x-c)=0, where a,b,c are the three zeroes of it. simplify and get the polynomial. ditto method for others.