document.write( "Question 1019225: Find the range of k for which x^2-(k+2)x+k+5=0, has two different negative solutions \r
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Algebra.Com's Answer #635184 by Edwin McCravy(20063)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"x%5E2-%28k%2B2%29x%2Bk%2B5\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "The solution using the quadratic formula:\r\n" );
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document.write( "simplifies to\r\n" );
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document.write( "\"%28k%2B2+%2B-+sqrt%28k%5E2-16%29%29%2F2\"\r\n" );
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document.write( "We only need to require that the larger\r\n" );
document.write( "solution, the one with the plus sign before\r\n" );
document.write( "the square root, be negative, so\r\n" );
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document.write( "\"%28k%2B2+%2B+sqrt%28k%5E2-16%29%29%2F2%3C0\" \r\n" );
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document.write( "The discriminant must be positive to prevent\r\n" );
document.write( "getting 1 single or 2 imaginary solutions, so \r\n" );
document.write( "setting the discriminant greater than 0,\r\n" );
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document.write( "\"k%5E2-16%3E0\"\r\n" );
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document.write( "That has solutions k < -4 or k > 4.\r\n" );
document.write( "If k > 4 then certainly the larger solution \r\n" );
document.write( "will be positive.\r\n" );
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document.write( "So we must take k < -4\r\n" );
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document.write( "\"%28k%2B2+%2B+sqrt%28k%5E2-16%29%29%2F2%3C0\"\r\n" );
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document.write( "Multiplying both sides by 2\r\n" );
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document.write( "\"k%2B2+%2B+sqrt%28k%5E2-16%29%3C0\"\r\n" );
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document.write( "\"sqrt%28k%5E2-16%29%3C-k-2\"\r\n" );
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document.write( "\"k%5E2-16+%3Ck%5E2%2B4k%2B4\"\r\n" );
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document.write( "\"-16+%3C4k%2B4\"\r\n" );
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document.write( "\"-20+%3C4k\"\r\n" );
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document.write( "\"-5%3Ck\"\r\n" );
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document.write( "Therefore to have both solutions negative,\r\n" );
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document.write( "\"-5%3Ck%3C-4\"\r\n" );
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document.write( "Edwin
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