document.write( "Question 1085951: For what negative value of k is there exactly one solution to this system of equations?
\n" ); document.write( "y=2x^2+kx+6
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Algebra.Com's Answer #700078 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "For what negative value of k is there exactly one solution to this system of equations?
\n" ); document.write( "y=2x^2+kx+6
\n" ); document.write( "y=-x+4
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document.write( "1.  Reduce the system to one single equation \r\n" );
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document.write( "    -x+4 = 2x^2 + kx + 6    (1)   (use substitution !).\r\n" );
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document.write( "2.   The system has exactly one solution if and only if the equation (1) has the unique solution.\r\n" );
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document.write( "3.   Simplify the equation (1):\r\n" );
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document.write( "     2x^2 + (k+1) + 2 = 0.\r\n" );
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document.write( "     Its discriminant is  = .\r\n" );
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document.write( "     The equation (1) has the unique solution if and only if the discriminant is zero: \r\n" );
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document.write( "      = 0  <====>   = 16  <====>  k + 1 = +/-4.\r\n" );
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document.write( "4.   There are 2 solutions for k:  a)  k = 4 - 1 = 3,   and   b)  k = -4 -1 = -5.\r\n" );
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document.write( "Answer. Negative value of k under the question is -5.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Ignore other tutor's solution, since it is WRONG.\r
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