a polynomial function p(x) with rational coefficients has the given roots. find two additional roots of p(x)=0. 14-sqrt6 and -5i
To find two additional roots of the polynomial function p(x), we need to find two more values of x such that p(x) = 0.
Since the polynomial has rational coefficients, complex conjugate roots will occur in pairs. This means that if -5i is a root, then its conjugate, 5i, must also be a root.
Thus, our additional roots are 14-sqrt(6), -5i, 5i.
Therefore, two additional roots of p(x) = 0 are 5i and 14-sqrt(6).