Question

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

Answer 1

-i, and (7 - 8i)

Explanation:

If a + bi is a root of P(x) = 0, then a – bi is also a root of P(x) = 0.

Since i and 7 + 8i are two roots of P(x) = 0, then –i and 7 – 8i are two additional roots of P(x) = 0.

Answer 2

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).