A polynomial function upper P left parenthesis x right parenthesis with rational coefficients has the given roots. Find two additional roots of upper P left parenthesis x right parenthesis equals 0. i and 7 + 8i

Given that a polynomial function P (x) has rational coefficients.

Two roots are already given which are i and 7+8i,

Now we have to find two additional roots of P (x) = 0

Given roots i and 7+8i are complex roots and we know that complex roots always occur in conjugate pairs so that means conjugate of given roots will also be the roots.

conjugate of a+bi is given by a-bi

So using that logic, conjugate of i is i

also conjugate of 7+8i is 7-8i

Hence final answer for the remaining roots are (-i) and (7-8i).