Respuesta :
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
[tex]k(x)=x(x+2)^3(x+4)^2(x-5)^4[/tex]
To find the roots of this function, we equate the function to zero.
[tex]x(x+2)^3(x+4)^2(x-5)^4=0[/tex]
We now use the zero product principle, to obtain;
[tex]x=0[/tex], with multiplicity 1
[tex](x+2)^3=0[/tex]
[tex]\Rightarrow x=-2[/tex], with multiplicity 3
[tex](x+4)^2=0[/tex]
[tex]\Rightarrow x=-4[/tex], with multiplicity 2
[tex](x-5)^4=0[/tex]
[tex]\Rightarrow x=5[/tex], with multiplicity 5.
Answer:
The roots of the function;
[tex]k(x)=x(x+2)^3(x+4)^2(x-5)^4[/tex]
- 0 has multiplicity 1.
- -2 has multiplicity 3.
- -4 has multiplicity 2.
- 5 has multiplicity 4.
Step-by-step explanation:
Given information:
The function;
[tex]k(x)=x(x+2)^3(x+4)^2(x-5)^4[/tex]
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 [tex]0[/tex]
[tex]x(x+2)^3(x+4)^2(x-5)^4=0[/tex]
As, [tex]x=0[/tex] , is having multiplicity [tex]1[/tex].
[tex](x+2)^3=0\\x=-2[/tex]
Having a multiplicity 3.
Now,
[tex](x+4)^2=0\\x=-4[/tex]
Having a multiplicity 2.
And,
[tex](x-5)^4=0\\x=5[/tex]
Having multiplicity 4.
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