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

Question

-5,-4,1-i√3

Answer 1

x= 1+isqr3

x-1 = isqr3

x^2-2x + 1 = -3

x^2 -2x +4= 0

f(x)= (x+4)(x+5)(x^2-2x+4)

= (x^2 +9x +20)(x^2 -2x +4)

= x^4 +7x^3 +6x^2 -4x +80