document.write( "Question 1209169: For what real values of k does the quadratic 12x^2 + kx + 27 = 0 have nonreal roots? Enter your answer as an interval. \n" ); document.write( "

Algebra.Com's Answer #847751 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "The quadratic equation 12x^2 + kx + 27 = 0 has nonreal roots if and only if its discriminant\r\n" );
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document.write( "    d = b^2 - 4ac\r\n" );
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document.write( "is negative\r\n" );
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document.write( "    k^2 - 4*12*27 < 0,\r\n" );
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document.write( "    k^2 < 4*12*27 = 4*3*4*3^3 = 3^4*4^2,\r\n" );
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document.write( "    |k| <  = 3^2*4 = 9*4 = 36,\r\n" );
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document.write( "    -36 < k < 36.\r\n" );
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document.write( "In the interval form, \"k\" should be in the interval (-36,36).    ANSWER\r\n" );
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