A polynomial function P(x) with rational coefficients has the given root. Find two additional roots of P(x) = 0
i and 7 + 8i
Since P(x) has rational coefficients, any complex roots must occur in conjugate pairs.
Given that i is a root, its conjugate -i must also be a root.
Similarly, since 7 + 8i is a root, its conjugate 7 - 8i must also be a root.
Thus, the two additional roots are -i and 7 - 8i.