Question

Determine the multiplicity of the roots of the function k(x) = x(x + 2)3(x + 4)2(x − 5)4. 0 has multiplicity −2 has multiplicity −4 has multiplicity 5 has multiplicity

Answer 1

>0 has multiplicity >>>>> 1

-2 has multiplicity  >>>>> 3

-4 has multiplicity >>>>>> 2

5 has multiplicity >>>>>> 4

Step-by-step explanation:

Answer 2

Answer:

0 has multiplicity 1

-2 has multiplicity 3

-4 has multiplicity 2

5 has multiplicity 4

Step-by-step explanation:

The multiplicity of the root of a polynomial function, refers to the number of time the root repeats itself.

The given function is

$k(x)=x(x+2)^3(x+4)^2(x-5)^4$

To find the roots of this function, we equate the function to zero.

$x(x+2)^3(x+4)^2(x-5)^4=0$

We now use the zero product principle, to obtain;

$x=0$, with multiplicity 1

$(x+2)^3=0$

$\Rightarrow x=-2$, with multiplicity 3

$(x+4)^2=0$

$\Rightarrow x=-4$, with multiplicity 2

$(x-5)^4=0$

$\Rightarrow x=5$, with multiplicity 5.