Question

The polynomial f(x) has degree 2. Choose each statement that could describe all the zeros of F

Answer 1

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 $x_1, x_2, \codts, x_n$ is given by:

$f(x) = a(x - x_1)^{n_1}(x - x_2)^{n_2} \cdots (x - x_n)^{n_n}$

• In which a is the leading coefficient and $n_1, n_2, \cdots, n_n$ 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 $n_1 = 2$.

• Two zeros with multiplicity 1, as the sum is $n_1 + n_2 = 1 + 1 = 2$

To learn more about the Factor Theorem, you can take a look at brainly.com/question/24380382