document.write( "Question 1209248: Find the constant k such that the quadratic 2x^2 + 3x - 20x + 3x^2 + k has a double root. \n" ); document.write( "
Algebra.Com's Answer #847909 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"2x%5E2+%2B+3x+-+20x+%2B+3x%5E2+%2B+k\"\r\n" );
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document.write( "\"5x%5E2+-+17x+%2B+k\"\r\n" );
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document.write( "It will have a double root if its discriminant b2-4ac = 0\r\n" );
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document.write( "\"discriminant+=+%28-17%29%5E2-4%285%29%28k%29+=+0\"\r\n" );
document.write( "\"289-20k+=+0\"\r\n" );
document.write( "\"-20k=-289\"\r\n" );
document.write( "\"k=%28-289%29%2F%28-20%29\"\r\n" );
document.write( "\"k=289%2F20\"    <-- answer\r\n" );
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document.write( "Checking:\r\n" );
document.write( "\"2x%5E2+%2B+3x+-+20x+%2B+3x%5E2+%2B+289%2F20=0\"\r\n" );
document.write( "\"5x%5E2+-+17x+%2B+289%2F20=0\"\r\n" );
document.write( "\"100x%5E2-340x%2B289=0\"\r\n" );
document.write( "\"%2810x-17%29%2810x-17%29=0\"\r\n" );
document.write( "10x-17=0;  10x-17=0\r\n" );
document.write( "   10x=17;    10x=17\r\n" );
document.write( "     x=\"17%2F10\";     x=\"17%2F10\"\r\n" );
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document.write( "So both roots are the same, so it has a double root if \"k=289%2F20\"\r\n" );
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document.write( "So \"k=289%2F20\" is correct.\r\n" );
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document.write( "Edwin
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