Question

P(x) with rational coefficients has the given roots (i and 7 + 8i) Find two additional roots?

Answer 1

P ( x ) has the given roots: ( i, 7 + 8 i ).
The complex roots of a polynomial P ( x ) with rational coefficients come in pair as:
a + b i and a - b i;
Additional roots are:  - i,   7 - 8 i.