Write a polynomial function ff of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. write the polynomial in standard form. 3, 4+2i, 1+7√3, 4+2i, 1+7
I am answering based on the assumption that the last zero is 1 + 7√3
FIRST, set up the zeros as factors: x=3 --> (x - 3)=0 x=4+2i --> [x - (4 + 2i)] = 0 don't forget the conjugate! (which is x=4-2i) --> [x - (4 - 2i)] = 0 x=1+7√3 --> [x - (1+7√3)] = 0 don't forget to rationalize it! (x=1-7√3) --> [x - (1-7√3)] = 0 x=4+2i was already given as a zero so this factor and its conjugate have a multiplicity of 2 (meaning it has an exponent of 2) x=1+7√3 was also previously given as a zero so it also has a multiplicity of 2.
