Question

suppose that a polynomial function of degree 5 with rational coefficients has the given numbers as zeros. find the other zero(s). -2/3,2/3,0,4-i

Answer 1

Answer: -2/3, 2/3, 0, 4-i, and 4+i.

Explanation:

A polynomial function of degree 5 with rational coefficients and the given zeros -2/3, 2/3, 0, and 4-i must have a complex conjugate of 4-i as another zero. Complex zeros of a polynomial with real coefficients always come in conjugate pairs. So, the other zero is 4+i.

Now we have all the zeros of the polynomial: -2/3, 2/3, 0, 4-i, and 4+i.