document.write( "Question 1160852: Find the possible value(s) for k if the quadratic 3x^2 -2kx +4k=0 has two real roots \n" ); document.write( "

Algebra.Com's Answer #784260 by ikleyn(52810) $\"\"$ $\"About$

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document.write( "The quadratic  3x^2 - 2kx + 4k  has two real roots if and only is the discriminant \r\n" );
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document.write( "    d = b^2 - 4ac is non-negative:  (-2k)^2 - 4*3*4k >= 0.\r\n" );
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document.write( "It inplies\r\n" );
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document.write( "    4k^2 - 48k >= 0\r\n" );
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document.write( "    k^2  - 12k >= 0\r\n" );
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document.write( "    k*(k - 12) >= 0\r\n" );
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document.write( "ANSWER.  EITHER k <=0  OR  k >= 12.\r\n" );
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document.write( "Note that when k = 0 or k = 12 (when d = 0), the two real roots merge into one real root of the multiplicity 2.\r\n" );
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