A fourth degree polynomial with real coefficients can have - 4, 8i,+4i, and as its zeros. True or false? Justify your answer.

Question

Ryland Moore

Mathematics

21 September, 03:37

A fourth degree polynomial with real coefficients can have - 4, 8i,+4i, and as its zeros. True or false? Justify your answer.

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Elisha · Answer 1

You didn't give the fourth zero, but the answer is still false. If you have a root or an imaginary number as a zero, then its conjugate is also a zero. So if 8i is a zero, then - 8i must also be a zero, and if 4i is a zero, then - 4i must be a zero, with those zeros and - 4, the number of zeroes exceeds the number of zeroes that a fourth degree polynomial can have.