Question

Find all of the zeros of the polynomial function and state the multiplicity of each.

f (x) = (x^2 – 16)^2

A. – 4 with multiplicity 2 and 4 with multiplicity 2

B. – 4i with multiplicity 2 and 4i with multiplicity 2

C. 4 with multiplicity 2

D. 4 with multiplicity 4

Answer 1

f(x) = (x²-16)²
= ((x+4)(x-4))²
= (x+4)²(x-4)²
Can you take it from here?

Answer 2

Yes this is what I got, is it correct?

C. 4 with multiplicity 2 ?

Answer 3

No, it is not the case. There are four roots for a quartic equation, so one single root with multiplicity of 2 does not suffice.

When you have the factor (x+4)², that implies x=-4 with multiplicity of 2.
If you repeat the process with the factor (x-4)², you will find the answer you need.

Answer 4

Wow I am confused now. So does the answer include the i? which is

B. – 4i with multiplicity 2 and 4i with multiplicity 2

OR

A. – 4 with multiplicity 2 and 4 with multiplicity 2

I am goin to say A but I could be wrong.

Answer 5

A is correct. The roots are real, so there is no i involved.
There are two distinct roots, ±4 each with multiplicity of 2. So A is the answer.