I need help with an algebra problem

Anonymous
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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

shyamnair3
School: New York University

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The factor theorem states that a polynomial $f(x)$ has a factor $(x - k)$ if and only if$f(k)=0$ (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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Review

Anonymous
Excellent job

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