Question

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

Answer 1

Answer:  The correct options are

(D) 6 with multiplicity 2

(F) -2 with multiplicity 2.

Step-by-step explanation:  We are given to find the roots of the following polynomial function :

$f(x)=(x-6)^2(x+2)^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know that

the roots of a polynomial p(x) are given by the equation p(x) = 0.

Therefore, the roots of the given polynomial (i) are given by

$f(x)=0\\\\\Rightarrow (x-6)^2(x+2)^2=0\\\\\Rightarrow (x-6)^2=0,~~~~~~(x+2)^2=0\\\\\Rightarrow x=6,6~~~~~~~~~~\Rightarrow x=-2,-2.$

Thus, the required roots are

6 with multiplicity 2 and -2 with multiplicity 2.

Options (D) and (F) are correct.

Answer 2

Answer:

6 with multiplicity 2

and

-2 with multiplicity 2