Question

Please help. Having a hard time with this.

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

I say it's A or C but leaning towards A? Any suggestions? Thanks!

Answer 1

(x²-16)²
=(x+4)²(x-4)²

What can you say with the number of distinct zeroes?
What can you say about the multiplicity of each zero?
The order of the polynomial being 4, what can you say about the total number of zeros, all multiplicities taken into account?

If the answer is either A or C, which one would you choose?

Answer 2

I was thinking (A) because of the -16, and we need a - number to get that. Is this right?

Answer 3

A is correct.
There are two distinct roots, so C and D are out of the question.
The zeroes are real, so B is out of the question. That leaves us with A.