document.write( "Question 1209299: For an integer n, the inequality
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Algebra.Com's Answer #848122 by ikleyn(52866) $\"\"$ $\"About$

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\n" ); document.write( "For an integer n, the inequality
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document.write( "The given inequality is equivalent to\r\n" );
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document.write( "    4x^2 + nx + 121 < 0.\r\n" );
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document.write( "It has no real solutions if and only if the discriminant \r\n" );
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document.write( "    d = b^2 - 4ac < 0\r\n" );
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document.write( "    n^2 - 4*4*121 < 0\r\n" );
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document.write( "    n^2 < 16*121\r\n" );
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document.write( "    |n| <  \r\n" );
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document.write( "    |n| < 4*11\r\n" );
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document.write( "    |n| < 44\r\n" );
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document.write( "    -44 < n < 44.\r\n" );
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document.write( "This inequality has  43 + 1 + 43 = 87 solutions in integer numbers.\r\n" );
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document.write( "ANSWER.  There are 87 different possible integer values of n such that\r\n" );
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document.write( "         the given inequality has no real solutions.\r\n" );
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