I need help with an algebra problem
Algebra

Tutor: None Selected  Time limit: 1 Day 
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
Thank you for the opportunity to help you with your question!

The factor theorem states that a polynomial has a factor if and only if (i.e. 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.




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

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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