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

2) x^3 - 4x^2 + x - 4
extra credit: why a cubic, not a quadratic?

4) x^3 - (6+√2)x^2 + (9+5√2)x - 4(1+√2)
minimum degree. To get rid of the √2, add a root of 1-√2 to get
x^4 - 7x^3 + 13x^2 - 3x - 4

Answer 2

-12-18i