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
Explanation & Answer
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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.
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