I need help with an algebra problem

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Use the Factor Theorem to determine a polynomial equation, of lowest degree, that has only the indicated roots:

1/3 is a double root,  -2 is a double root. 

The answer should be 9x^4 +30x^3 +13x^2 -20x +4 = 0  

I just need to know how to do the work to get to that answer. Thanks 

Nov 6th, 2015

Thank you for the opportunity to help you with your question!

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The factor theorem states that a polynomial f(x) has a factor (x - k) if and only iff(k)=0 (i.e. k is a root).

1/3 is a double root, -2 is a double root

So the factors are

(x - 1/3),

(x - 1/3), (because it is a double root we have to include it twice)

(x - (-2)) = (x +2) and

(x - (-2)) = (x +2) (because it is a double root we have to include it twice)


So to get the polynomial multiply the factors.

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I will submit the remaining  answer within 10 minutes. Sorry for the delay.

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Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 6th, 2015

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Nov 6th, 2015

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I made a mistake in the last step. It should be +10/3 x^3 and not -10/3 x^3. Please correct it.

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To get the answer that you have mentioned, put f(x) = 0 and multiply throughout by 9. Multiplying by a constant will not change the zeroes or roots.


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Nov 6th, 2015

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