A polynomial function P(x) with rational coefficients has the given roots. Find two additional roots of p(x)=0.
7- sqrt 3 and 8i
Since the polynomial has rational coefficients, the complex roots must come as conjugate pairs. Thus, if 8i is a root, then -8i must also be a root.
Therefore, the roots of the polynomial are:
7 - sqrt 3, 8i, -8i, and two additional roots.
To find the two additional roots, we can use the fact that if a polynomial has rational coefficients, then any irrational root must come with its conjugate.
Therefore, since 7 - sqrt 3 is an irrational root, its conjugate, 7 + sqrt 3, must also be a root.
So the two additional roots are:
7 + sqrt 3 and -8i.