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charity1972

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Aug 20, 2010
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find the zeros of the polynomial function and state multiplicityof each...

f(x)=x^4-20x^2+64
 


What are you currently studying in class ? Are you supposed to use the Rational Roots Theorem and polynomial division, to first factor this polynomial ?

There is also a way to do it with "u substitution", to first form a quadratic equation, instead.

I don't know which methods you're learning. Please explain why you're stuck, or show what you've done thus far, so that I can see what's going on. 8-)

 
we can use the u thing...lol i am having complete trouble with all of it....this problem is on a take home midterm, i have several more...lol
 
this is what is says,
use composition of functions to determine whether or not the given funtions are inverse of each other. show your work
 


:?: Are you supposed to do this: "find the zeros of the polynomial function and state multiplicityof each"

 


Okay, maybe the instruction about inverses pertains to something else. (Please start a new thread for each new exercise.)

If we let x^2 = u, then we can rewrite the polynomial.

u^2 - 20u + 64

Can you factor this?

 


I hope you mean the following.

(u - 4)(u - 16)

Now, we reverse the u-substitution. u is the same as x^2.

(x^2 - 4)(x^2 - 16)

Each of these factors is a Difference of Squares. Factor them.

Then, set each of the four factors equal to zero, and solve for x.

 


I was willing to get you started on your take-home midterm, but I cannot help you complete the exam.

If you need to refresh your memory, there are some basic lessons at purplemath.com.

 
\(\displaystyle f(x) \ = \ x^4-20x^2+64\)

\(\displaystyle By \ grouping, \ we \ get \ x^4-16x^2-4x^2+64 \ = \ f(x) \ = \ x^2(x^2-16)-4(x^2-16)\)

\(\displaystyle Hence, \ f(x) \ = \ (x^2-16)(x^2-4) \ = \ (x-4)(x+4)(x-2)(x+2).\)
 
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