Mathematics, 02.01.2020 05:31 rachaelpovosky8

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

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Answer from: Enyo07

The roots of the function;

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

0 has multiplicity 1.-2 has multiplicity 3.-4 has multiplicity 2.5 has multiplicity 4.

Step-by-step explanation:

Given information:

The function;

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

As, we know that multiplicity of any function is defined as the number of times the roots repeats in the solution.

Hence, we need to find the roots of the function

So, equating the function to

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

As, x=0 , is having multiplicity .

$(x+2)^3=0\\x=-2$

Having a multiplicity 3.

Now,

$(x+4)^2=0\\x=-4$

Having a multiplicity 2.

And,

$(x-5)^4=0\\x=5$

Having multiplicity 4.

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Answer from: chandra99

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.

Answer from: Quest

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

Answer from: Quest

d. vertex

step-by-step explanation:

Multiple choice: select the best answer and click "submit." what is the name of the sides of the t

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