Question

Suppose that the polynomial function f is defined as follows.f (x) = (x+6)²(x-7)2(x - 5)3List each zero of faccording to its multiplicity in the categories below.If there is more than one answer for a multiplicity, separate them with commas. If there is no answer, click on "None."Zero(s) of multiplicity one:믐None00Zero(s) of multiplicity two:х?Zero(s) of multiplicity three:

Answer 1

The polynomila function is,

$f(x)=(x+6)^2(x-7)^2(x-5)^3$

For the zeros of the function f(x) = 0. So,

$(x+6)^2(x-7)^2(x-5)^3=0$

So zeros of the function are x = -6, x = 7 and x = 5.

The multiplicity of zero, x = -6 is two as factor (x + 6) is raised with power of 2. Simillarly, multiplicity of zero, x = 7 is 2 and multiplicity of zero x = 5 is 3.

Answer:

Zero(s) of multiplicity one: None

Zero(s) of multuiplicity two: -6,7

Zero(s) of multipicity three: 5