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12 days ago

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

Mathematics

2 answers:

Leona [9.2K]12 days ago

5 0

Answer:

Multiplicity for 0 is 1

Multiplicity for -2 is 3

Multiplicity for -4 is 2

Multiplicity for 5 is 4

zzz [9K]12 days ago

4 0

Answer:

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

To ascertain the multiplicity of 0, -2, -4, 5.

The multiplicity refers to how many times a root appears in a function.

First, identify the function's roots by setting it to zero.

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

Thus, the roots are x=0, -2, -4, and 5

To determine the roots' multiplicities:

The factor of x will give a root of x=0 with a multiplicity of 1

likewise, x=-2 with a multiplicity of 3

x=-4 with a multiplicity of 2

and x=5 with a multiplicity of 4.

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