Use the given zeros of a polynomial with degree 6 whose coefficients are real numbers to find the remaining zeros of the polynomial, -6+13i^3, -8+s^2i, -3-4i (where s is a real number)

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justaguide eNotes educator| Certified Educator

The polynomial has a degree 6 and real coefficients. The zeros of the polynomial given are -6+13i^3, -8+s^2*i and -3-4i

As the coefficients of the polynomial are real the complex roots occur in conjugate pairs. This gives the roots as -6-13i, -6+13i, -8+s^2*i, -8-s^2*i, -3-4i and -3+4i

From the given information it is not possible to determine the value of s as it can take on any value and the other conditions would remain the same.

The roots of the polynomial can only be given as -6-13i, -6+13i, -8+s^2*i, -8-s^2*i, -3-4i and -3+4i where s is a real number.