document.write( "Question 1094972: Find k so that the roots of (2k-1)x^2 + (k-1)x - 16 = 0 are numerically equal but opposite in sign. \n" ); document.write( "

Algebra.Com's Answer #709556 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "If \"the roots are numerically equal but opposite in sign\", it means that the sum of roots is ZERO.\r\n" );
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document.write( "From the other side, according to Vieta's theorem, the sum of the roots of the quadratic polynomial is equal to its coefficient at \"x\", \r\n" );
document.write( "taken with the opposite sign and divided by the leading coefficient.\r\n" );
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document.write( "It means that the coefficient at \"x\" must be equal to ZERO.\r\n" );
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document.write( "Hence, k = 1.\r\n" );
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document.write( "Answer.  The necessary and sufficient condition is k = 1.\r\n" );
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