Question
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)
Responses
5
5
6
6
4
4
8
Responses
5
5
6
6
4
4
8
Answers
GPT-4o mini
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**.
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**.