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)(x4))^{2}
= (x+4)^{2}(x4)^{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 (x4)^{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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