Question

Suppose that the polynomial function is defined as follows. f(x) = 4(x -11) (x + 9) (x - 5)^3List each zero of according to its multiplicity in the categories below. If there is more than one answer for a multiplicity, separate them with commas. If there is no answer, click on "None." Zero(s) of multiplicity one:_________Zero(s) of multiplicity two:_________ Zero(s) of multiplicity three:_________

Answer 1

Answer:

Zero(s) of multiplicity one: 11,-9

Zero(s) of multiplicity two: None

Zero(s) of multiplicity three: 5

Step-by-step explanation:

Suppose that we have a polynomial function in the following format:

$f(x) = a*(x - x_{0})^{m_{0}}*(x - x_{1})^{m^{1}}*...*(x - x_{n})^{m^{n}}$

The zeros are $x_{0}, x_{1}, ..., x_{n}$.

The multiplicites are $m_{0}, m_{1},..., m_{n}$

In this question:

f(x) = 4(x -11) (x + 9) (x - 5)^3

So

11 is a zero of multiplicity 1

-9 is a zero of multiplicity 1

5 is a zero of multiplicity 3.

So the answer is:

Zero(s) of multiplicity one: 11,-9

Zero(s) of multiplicity two: None

Zero(s) of multiplicity three: 5