Does there exist a polynomial of degree 3 with real coefficients that has zeros 5 , - 5, and i ?
A)yes
B)no

Name: Does there exist a polynomial of degree 3 with real coefficients that has zeros 5 , - 5, and i ? A)yes B)no
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Question

Quizplus · Accepted Answer

A polynomial with real coefficients must have complex roots in conjugate pairs. Since i is a root, -i must also be a root for the polynomial to have real coefficients. Therefore, a polynomial of degree 3 with real coefficients cannot have 5, -5, and i as its roots.

Does There Exist a Polynomial of Degree 3 with Real