Question

What is the least degree of a polynomial equation that has 3i as a root with a multiplicity of 5 and 3 as a root with a multiplicity of 5?

A) 2
B) 5
C) 6
D) 10

Answer 1

The least degree of the polynomial equation with 3i and 3 as roots, both with a multiplicity of 5, is 5.

Step-by-step explanation:

To find the polynomial equation with 3i as a root with a multiplicity of 5 and 3 as a root with a multiplicity of 5, we know that complex roots occur in conjugate pairs. Therefore, we can say that the polynomial will also have -3i as a root with a multiplicity of 5. Since the roots 3i, -3i, and 3 all occur with a multiplicity of 5, the polynomial will have a degree of 5.