document.write( "Question 1177575: The quadratic equation x² + kx + 36=0 has\r
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Algebra.Com's Answer #806666 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " I will show you a STANDARD and very SIMPLE WAY, \r
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document.write( "Since the problem talks about different real roots of a quadratic equation, it means that its discriminant is positive.\r\n" );
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document.write( "The discriminant is  b^2 - 4ac = k^2 - 4*36 = k^2 - 144.\r\n" );
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document.write( "So, the discriminant must be positive\r\n" );
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document.write( "    k^2 - 144 > 0.\r\n" );
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document.write( "It implies\r\n" );
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document.write( "    k^2 > 144, \r\n" );
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document.write( "which means that  EITHER k > 12  OR  k < - 12.\r\n" );
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document.write( "ANSWER.  The set of all possible values of k is  { k |  k > 12  or  k < - 12 }.\r\n" );
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document.write( "         It is the union of two infinite semi-intervals  (-oo,12) U (12,oo).\r\n" );
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