Algebra.Com's Answer #849845 by ikleyn(52909)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( "Find a monic quartic polynomial f(x) with rational coefficients whose roots
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document.write( "include x = 2 - i \sqrt[3]{3}$. Give your answer in expanded form.
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document.write( "The solution in the post by @CPhill is INCORRECT.\r
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document.write( " , I am not sure whether he correctly interprets x = 2 - i \sqrt[3]{3}$ in the condition \r\n" );
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document.write( "as 2 - i∛3. This fragment of the condition is, actually, UNREADABLE in this forum format, \r\n" );
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document.write( "so I ask you to write your formulas in plain text format, to avoid misreading.\r\n" );
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document.write( " , if to take this interpretation of @CPhill, then in the process of the solution he makes \r\n" );
document.write( "a fatal error.\r\n" );
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document.write( "Indeed, he writes in his post\r\n" );
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document.write( " **3. Eliminate the Cube Root:**\r\n" );
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document.write( " To get rational coefficients, we need to eliminate the ∛9 term. Let's call the quadratic factor we just found \r\n" );
document.write( " g(x) = x² - 4x + 4 + ∛9. To eliminate the cube root, we'll work with the equation ∛9 = -x² + 4x - 4, and cube both sides:\r\n" );
document.write( " 9 = (-x² + 4x - 4)³\r\n" );
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document.write( "It is totally wrong. From g(x) = x² - 4x + 4 + ∛9, we only can express ∛9 = g(x) - (x² - 4x + 4),\r\n" );
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document.write( "but this way will lead us to NOWHERE.\r\n" );
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document.write( "So, it is the point, where @CPhill makes this fundamental error, which ruines all his solution to dust.\r
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document.write( "My condolences. Ignore the solution by @CPhill, since it is IRRELEVANT and leads you to NOWHERE.\r
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