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 4 4 8 8 6 6
Answers
GPT-4o mini
According to the Fundamental Theorem of Algebra, the degree of a polynomial is determined by the number of its roots, counting multiplicities.
In this case, you have:
- One x-intercept with a multiplicity of 2 (which counts as 2 roots).
- Four imaginary solutions (which account for 4 roots).
So, the total number of roots (counting multiplicities) would be:
- 2 (from the x-intercept) + 4 (imaginary solutions) = 6.
Therefore, the degree of the polynomial function must be 6.
The correct answer is **6**.
In this case, you have:
- One x-intercept with a multiplicity of 2 (which counts as 2 roots).
- Four imaginary solutions (which account for 4 roots).
So, the total number of roots (counting multiplicities) would be:
- 2 (from the x-intercept) + 4 (imaginary solutions) = 6.
Therefore, the degree of the polynomial function must be 6.
The correct answer is **6**.