leading coefficient of 1, and zeros 3, and 4+i

Question

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

3, 4+i

Answer 1

p(x)=(x-3)(x-4-i)(x-4+i) (Since coefficients of the polynomial are rational, conjugate of 4+i (4-i) is also a zero for the polynomial).

p(x)= (x-3)((x-4)²+1)

      =  x³- 11 x² +41x-51. (degree 3)