Posted by **Breanna** on Monday, July 20, 2009 at 9:20pm.

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

- Algebra -
**MathMate**, Monday, July 20, 2009 at 9:59pm
f(x) = (x^{2}-16)^{2}

= ((x+4)(x-4))^{2}

= (x+4)^{2}(x-4)^{2}

Can you take it from here?

- Algebra -
**Breanna**, Monday, July 20, 2009 at 10:39pm
Yes this is what I got, is it correct?

C. 4 with multiplicity 2 ?

- Algebra -
**MathMate**, Monday, July 20, 2009 at 10:47pm
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.

- Algebra -
**Breanna**, Monday, July 20, 2009 at 11:23pm
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.

- Algebra -
**MathMate**, Tuesday, July 21, 2009 at 7:24am
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.

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