Find the root(s) of f (x) = (x- 6)2(x + 2)2.
-6 with multiplicity 1
-6 with multiplicity 2
6 with multiplicity 1
6 with multiplicity 2
-2 with multiplicity 1
-2 with multiplicity 2
2 with multiplicity 1
2 with multiplicity 2

6 with multiplicity 2

-2 with multiplicity 2

Step-by-step explanation:

We have given that find the roots of:

f (x) = (x- 6)²(x + 2)²

Note that the polynomials are already in the factored form. So we will only make it equal to zero

(x-6)² = 0

The square tells us that the root repeat twice

Move -6 to the R.H.S

Then,

x=6 , 6

(x+2)²=0

Move 2 to the R.H.S

Then,

x= -2, -2

Therefore the correct options are:

6 with multiplicity 2

-2 with multiplicity 2