According to the Fundamental Theorem of Algebra, what must be the degree of a polynomial function with one x-intercept that has a multiplicity of two and four imaginary solutions?(1 point)

Question

Responses

5
5

6
6

4
4

8

Answer 1

According to the Fundamental Theorem of Algebra, the degree of a polynomial is equal to the number of complex roots (including multiplicities) it has.

In this case, you have:

• One x-intercept with a multiplicity of two, which counts as two roots.
• Four imaginary solutions, which are also counted as roots.

Adding these together:

• 2 (from the x-intercept with multiplicity) + 4 (imaginary solutions) = 6 roots total.

Therefore, the degree of the polynomial function is 6.

So the correct answer is 6.