I need help with an algebra problem

timer Asked: Nov 6th, 2015
account_balance_wallet $5

Question Description

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 

Tutor Answer

School: New York University

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


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.


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


Please let me know if you need any clarification. I'm always happy to answer your questions.

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