document.write( "Question 1180426: Determine the value(s) of m so that the quadratic equation mx^2+6x = −m has no real roots. \n" ); document.write( "

Algebra.Com's Answer #810083 by ikleyn(52800) $\"\"$ $\"About$

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\n" ); document.write( "Determine the value(s) of m so that the quadratic equation mx^2+6x = −m has no real roots.
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document.write( "Write the equation in equivalent standard form\r\n" );
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document.write( "    mx^2 + 6x + m = 0\r\n" );
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document.write( "It HAS NO real roots if and only if the discriminant of the equation is negative\r\n" );
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document.write( "    b^2 - 4ac < 0,   or\r\n" );
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document.write( "    6^2 - 4m^2 < 0,\r\n" );
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document.write( "    36 < 4m^2\r\n" );
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document.write( "     9 < m^2\r\n" );
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document.write( "     m^2 > 9\r\n" );
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document.write( "     which is equivalent  to  { m < -sqrt(9) = -3   OR   m > sqrt(9) = 3 }.\r\n" );
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document.write( "ANSWER.  m < -3  OR  m > 3.\r\n" );
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