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 2 years ago
A cubic polynomial with rational coefficients has the roots 6 + square root 6 and 2/3. Find one additional root.
 2 years ago
A cubic polynomial with rational coefficients has the roots 6 + square root 6 and 2/3. Find one additional root.

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freewilly922
 2 years ago
Best ResponseYou've already chosen the best response.0Since it has rational coefficients, that means that when you multiply the product of the three roots \[(a)(x(6+\sqrt{6}))(x2/3)\] you somehow avoid having an irrational coefficient (something with a square root). So the big question is What times (x(6+sqrt(6))) will avoid this issue. I believe there is a parallel problem with complex numbers and they multiply by the complex conjugate. I suspect something similar here.
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