A polynomial of degree 6 has real coefficients.What are the remaining roots if the roots given are: -8 + 11*i, -7 + 17*i, 16 - i*sqrt 2

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The polynomial of degree 6 has 6 roots. The polynomial that is being considered has roots -8 + 11*i, -7 + 17*i, 16 - i*sqrt 2.

All complex roots of a polynomial are found in conjugate pairs to ensure that the coefficients are real. If this were not the case, the coefficients would not be real numbers.

For -8 + 11*i, the polynomial has a root -8 - 11*i

-7 + 17*i gives another root complex root -7 - 17*i and as 16 - i*sqrt 2 is a root there is another root equal to 16 + i*sqrt 2

The other roots of the polynomial are : -8 - 11*i, -7 - 17*i, 16 + i*sqrt 2

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial