document.write( "Question 408298: Calculate the smallest positive integer k for which the equation (kx+1)^2=8x has no real roots. \n" ); document.write( "
Algebra.Com's Answer #287706 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "            (kx+1)² = 8x\r\n" );
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document.write( "     k²x² + 2kx + 1 = 8x\r\n" );
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document.write( "k²x² + 2kx - 8x + 1 = 0\r\n" );
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document.write( " k²x² + (2k-8)x + 1 = 0\r\n" );
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document.write( "Compare to ax² + bx + c = 0\r\n" );
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document.write( "a = k², b = 2k-8,  c = 1 \r\n" );
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document.write( "For the solutions to have no real roots, the  \r\n" );
document.write( "discriminant must be negative, that is, less than zero.\r\n" );
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document.write( "Discriminant = b²-4ac = (2k-8)² - 4k²(1) = 4k²-32k+64 - 4k² = -32k+64\r\n" );
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document.write( "  -32k+64 < 0\r\n" );
document.write( "     -32k < -64\r\n" );
document.write( "        k > 2\r\n" );
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document.write( "Therefore the smallest positive integer k for which the equation\r\n" );
document.write( "(kx+1)^2=8x has no real roots is 3.\r\n" );
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document.write( "[Notice: I changed your word \"biggest\" to \"smallest\", for every value\r\n" );
document.write( "of k greater than 2 will cause the equation to have no real roots, even \r\n" );
document.write( "if k were ten million trillion!  If the problem had \"biggest\" there\r\n" );
document.write( "instead of \"smallest\", then the problem was botched.  Point this out\r\n" );
document.write( "to your teacher.]  \r\n" );
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document.write( "Edwin
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