Answer:
The zeros are: -5, -2 and 1.
Multiplicity of the zero -5 is three
Multiplicity of the zero -2 is two.
Multiplicity of the zero 1 is one.
Step-by-step explanation:
The zeros of a polynomial, [tex]f(x)[/tex], are those values of 'x' for which [tex]f(x)=0[/tex]
Given:
The polynomial is given as:
[tex]f(x)=-2(x-1)(x+2)^2(x+5)^3[/tex]
In order to find its zeros, we need to equate its factors to 0 and determine the values of 'x' for which the function becomes 0.
The factors of the polynomial are [tex](x-1),(x+2)^2,(x+5)^3[/tex]
So, equating each of them to 0, we get:
[tex](x+5)^3=0\\(x+5)(x+5)(x+5)=0\\x=-5,-5,-5\\\\(x+2)^2=0\\(x+2)(x+2)=0\\x=-2,-2\\\\(x-1)=0\\x=1[/tex]
Therefore, the zeros of the polynomial are -5, -2 and 1 with -5 repeated 3 times, -2 repeated 2 times and 1 occurring only once.
So, multiplicity of -5 is 3, multiplicity of -2 is 2 and multiplicity of 1 is 1.
