Pls Help!!!

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

Question

Answered

Verified Answer :

ColinJacobus ColinJacobus · Answer 1 · 2019-03-07T13:44:28-05:00

Answer: The answer is given below.

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

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

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.

erinna erinna · Answer 2 · 2021-10-28T04:37:13-04:00

The roots of a given function are \(0,-2,-4,5\) with multiplicity \(1,3,2,4\) respectively.

Given:

The given function is \(k(x)=x(x+2)^3(x+4)^2(x-5)^2\).

To find:

The multiplicity of the roots of the given function.

Explanation:

The factored form of a polynomial is:

\(P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}\)

Where, a is a constant, \(c_1,c_2,...,c_n\) are roots with multiplicity \(m_1,m_2,..,m_n\).

The given function can be written as:

\(k(x)=(x-0)^1(x-(-2))^3(x-(-4))^2(x-5)^2\)

Therefore, the roots of a given function are \(0,-2,-4,5\) with multiplicity \(1,3,2,4\) respectively.

Learn more:

https://brainly.com/question/12475624