Question

Which answer choice best represents a degree n polynomial whose zeros include: - 4 (with multiplicity 2), 20, i, and - 3+i along with any other complex zeros?A. Degree: 7; Other zeros: -i and -3- i B. Degree: 5; Other zeros: i and - 3+ i C. Degree: 7; Other zeros: -i and 3 - i D. Degree: 7; Other zeros:i and - 3 + i

Answer 1

Degree 7

Other zeros -i and -3-i (option A)

Here, we want to give the degree of the polynomial

The degree of a polynomial simply refer to the number of roots that the polynomial have

With respect to this question, we have the following roots

-4, since it is with a multiplicity of 2, it means we have two roots here (-4,-4)

20

i

-3+i

The other complex roots are simply the conjugates of the given complex roots

This should be -i and -3-i

So the total number of roots are 7 and also, the degree which is the number of roots is also seven; meaning we have a polynomial of degree 7