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

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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

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