document.write( "Question 304980: Find the values of K such that the equation 3x^2 + 10x + K =0 has imaginary roots.\r
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Algebra.Com's Answer #218409 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You said you thought the answer is \"25%2F3\".  NO!  There are infinitely\r\n" );
document.write( "many answers, not just one.  Notice the word \"valueS\", with an \"S\", \r\n" );
document.write( "not \"value\". So your answer must be incorrect.  You must\r\n" );
document.write( "answer with an inequality or with a set in interval notation. \r\n" );
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document.write( "\"3x%5E2+%2B+10x+%2B+K+=0\"\r\n" );
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document.write( "\"DISCRIMINANT+=+B%5E2+-+4AC+=+10%5E2-4%283%29%28K%29+=+100-12K\"\r\n" );
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document.write( "For the roots to be imaginary this must be negative, which\r\n" );
document.write( "is the same as less than zero, so we set \"100-12K\" less\r\n" );
document.write( "than zero.\r\n" );
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document.write( "\"100-12K%3C0\"\r\n" );
document.write( "\"-12K%3C-100\"\r\n" );
document.write( "\"%28-12K%29%2F%28-12%29+%3E%28-100%29%2F%28-12%29\"\r\n" );
document.write( "\"K+%3E+25%2F3\" [Note that the inequality reversed because we divided by a negative number] \r\n" );
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document.write( "The answer is the set of real numbers GREATER THAN \"25%2F3\".\r\n" );
document.write( "So \"25%2F3\" is not even an answer at all, since \"25%2F3\" is\r\n" );
document.write( "not greater than itself!!!!\r\n" );
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document.write( "The answer is that K is in the interval \"%22%5B%22\"\"25%2F3\"\"%22%2C%22\"\"infinity\"\"%22%29%22\"  \r\n" );
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document.write( "Edwin
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