Using the Factor Theorem, it is found that the statements that could describe all zeros of F are:
- One zero with multiplicity 2.
- Two zeros with multiplicity 1.
What is the Factor Theorem
- The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)^{n_1}(x - x_2)^{n_2} \cdots (x - x_n)^{n_n}[/tex]
- In which a is the leading coefficient and [tex]n_1, n_2, \cdots, n_n[/tex] is the multiplicity of each zero.
- Then, for a function of the nth degree, the sum of the multiplicities of the zeros have to be n.
In this problem:
- A 2nd degree polynomial is desired.
Then, the correct statements are:
- One zero with multiplicity 2, as the sum is [tex]n_1 = 2[/tex].
- Two zeros with multiplicity 1, as the sum is [tex]n_1 + n_2 = 1 + 1 = 2[/tex]
To learn more about the Factor Theorem, you can take a look at https://brainly.com/question/24380382
