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
Help please!

Answer 1

Any zeros which include i must be balanced by another which has -i in its place. Any square roots must be balanced by another which has -(sqrt) in their place. Then, just write it as (x-zeros)

Answer 2

Im still not fully understanding

Answer 3

OK. If "a" is a zero, (x-a) is a factor. However, because all coefficients must be rational, sometimes you have to add in zeros to make sure the polynomial stays real and rational.

Answer 4

For example, (x-i) would make the entire polynomial imaginary unless you also had (x+i) to balance it out. The multiplication (x-i)(x+i)=x^2+i-i+1=x^2+1 gives real, rational coefficients.