Answer:
3,3,3,3 ,-6, and -6.
Step-by-step explanation:
Given the polynomial function
f(x) = [tex](x-3)^4(x+6)^2[/tex]
To find the roots of given polynomial we put f(x)=0
[tex](x-3)^4(x+6)^2[/tex]=0
Then we put
[tex](x-3)^4=0[/tex] and [tex](x+6)^2=0[/tex]
Now, we put each factor of (x-3 )equal to zero
x-3=0
x=3
x-3=0
x=3
x-3=0
x=3
x-3=0
x=3
Similarly , we put each factor of (x+6 ) equal to zero
Then we get
x+6=0
x=-6
x+6=0
x=-6
Multiplycity of 3=4
Multiplicity of -6= 2.
Multiplicity of any number is defined as the number of repeatation of that number in polynomial function.
Therefore, the roots of given polynomial function are 3,3,3,3-6 and -6.
