Pls !
determine the multiplicity of the roots of the function k(x) = x(x + 2)3(x + 4)2(x − 5)4.

The answer is given below.

Step-by-step explanation: We are given to find the multiplicity of the roots of the following equation:

We can clearly say that the roots of the above equation are 0, -2, -4 and 5.

The power of (x-0) is 1, so the multiplicity of 0 is 1.

The power of (x+2) is 3, so the multiplicity of -2 is 3.

The power of (x+4) is 2, so the multiplicity of -4 is 2.

The power of (x-5) is 4, so the multiplicity of 5 is 4.

Hence completed.