document.write( "Question 1175454: Find a cubic polynomial with integer coefficients that has \"matrix%282%2C1%2C%22%22%2C+2%5E%281%2F3%29%2B4%5E%281%2F3%29%29++\" as a root.\r
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\n" ); document.write( "\n" ); document.write( "I've been working on this question for some time, but I haven't made any headway. Can somebody write a solution to this? \n" ); document.write( "
Algebra.Com's Answer #801101 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We don't turn away \"advanced\" students if we can solve what they post.  Only\r\n" );
document.write( "Ikleyn does that. When she does that she removes it from the list of unsolved\r\n" );
document.write( "problems. That blocks other tutors from seeing the problem unless they visit\r\n" );
document.write( "the recently solved ones. Luckily I checked that today.  I don't always.\r\n" );
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document.write( "This involves Cardano's cubic formula for the solution to x³+px+q=0, which is\r\n" );
document.write( "not all that advanced. It only involves roots, which anyone in pre-calc can handle.\r\n" );
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document.write( "Cardano's formula for the solution for x³+px+q=0 is\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"root%283%2C-q%2F2%2Bsqrt%28q%5E2%2F4%2Bp%5E3%2F27%29%29\"\"%22%22%2B%22%22\"\"root%283%2C-q%2F2-sqrt%28q%5E2%2F4%2Bp%5E3%2F27%29%29\" \r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C+2%5E%281%2F3%29%2B4%5E%281%2F3%29%29++\"\"matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29\"\"matrix%282%2C1%2C%22%22%2Croot%283%2C2%29%2Broot%283%2C4%29%29\"\r\n" );
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document.write( "So we try to find p and q so that what's under one cube root equals 2 and\r\n" );
document.write( "what's under the other one equals 4.\r\n" );
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document.write( "So set \"-q%2F2%2Bsqrt%28q%5E2%2F4%2Bp%5E3%2F27%29\" equal to 2 and it will simplify to\r\n" );
document.write( "an equation in p3 and q.\r\n" );
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document.write( "Then set \"-q%2F2-sqrt%28q%5E2%2F4%2Bp%5E3%2F27%29\" equal to 4 and it will also simplify to\r\n" );
document.write( "an equation in p3 and q.\r\n" );
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document.write( "Then from those two equations, you can find integers for p and q.\r\n" );
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document.write( "Then the answer will be x3 + px + q.\r\n" );
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document.write( "If you need more help, ask for it in the form below, and I'll get back to you\r\n" );
document.write( "by email.\r\n" );
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document.write( "Edwin
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