document.write( "Question 87224: find the quadratic equation when one root is the square of the other \n" ); document.write( "
Algebra.Com's Answer #63180 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
find the quadratic equation when one root \r\n" );
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document.write( "There are infinitely many such quadratic \r\n" );
document.write( "equations, not just one!\r\n" );
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document.write( "If one root is r and the other r², then \r\n" );
document.write( "let's solve it backward:\r\n" );
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document.write( "We end up with \r\n" );
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document.write( "x = r and x = r²\r\n" );
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document.write( "Before that we'd have\r\n" );
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document.write( "x - r = 0 and x - r² = 0\r\n" );
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document.write( "Before that we'd have\r\n" );
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document.write( "(x - r)(x - r²) = 0\r\n" );
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document.write( "Before that we'd have\r\n" );
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document.write( "x² - r²x - rx + r³ = 0\r\n" );
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document.write( "or \r\n" );
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document.write( "x² - rx(r-1) + r² = 0\r\n" );
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document.write( "or\r\n" );
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document.write( "x² - r(r-1)x + r³ = 0\r\n" );
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document.write( "Before that we could have had any common\r\n" );
document.write( "factor k to have divided through by, so we\r\n" );
document.write( "would have had\r\n" );
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document.write( "kx² - kr(r-1)x + kr² = 0\r\n" );
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document.write( "Here are a bunch of examples of different quadratic \r\n" );
document.write( "equations all having one root as the square \r\n" );
document.write( "of the other:\r\n" );
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document.write( " x² - 110x + 1000 = 0 has roots 10 and 100\r\n" );
document.write( "8x² - 720x + 5832 = 0 has roots 9 and 81\r\n" );
document.write( "8x² - 48x - 216 = 0 has roots -3 and 9\r\n" );
document.write( "5x² - 150x - 1080 = 0 has roots -6 and 36\r\n" );
document.write( " x² - 30x - 216 = 0 has roots -6 and 36\r\n" );
document.write( " x² - 6x - 27 = 0 has roots -3 and 9\r\n" );
document.write( "2x² - 84x - 686 = 0 has roots -7 and 49\r\n" );
document.write( "5x² - 150x + 625 = 0 has roots 5 and 25\r\n" );
document.write( "6x² - 72x + 162 = 0 has roots 3 and 9\r\n" );
document.write( "9x² - 18x - 72 = 0 has roots -2 and 4\r\n" );
document.write( "8x² - 336x + 1728 = 0 has roots 6 and 36\r\n" );
document.write( "7x² - 630x + 5103 = 0 has roots 9 and 81\r\n" );
document.write( "7x² - 42x + 56 = 0 has roots 2 and 4\r\n" );
document.write( "4x² - 288x + 2048 = 0 has roots 8 and 64\r\n" );
document.write( "7x² - 140x - 875 = 0 has roots -5 and 25\r\n" );
document.write( "8x² - 96x + 216 = 0 has roots 3 and 9\r\n" );
document.write( "6x² - 12x + 6 = 0 has roots 1 and 1\r\n" );
document.write( "2x² - 4x + 2 = 0 has roots 1 and 1\r\n" );
document.write( "2x² - 12x + 16 = 0 has roots 2 and 4\r\n" );
document.write( "7x² - 504x - 5103 = 0 has roots -9 and 81\r\n" );
document.write( "9x² - 180x - 1125 = 0 has roots -5 and 25\r\n" );
document.write( "6x² - 432x - 4374 = 0 has roots -9 and 81\r\n" );
document.write( "2x² - 12x - 54 = 0 has roots -3 and 9\r\n" );
document.write( "7x² - 294x - 2401 = 0 has roots -7 and 49\r\n" );
document.write( "7x² - 294x - 2401 = 0 has roots -7 and 49\r\n" );
document.write( "4x² - 24x + 32 = 0 has roots 2 and 4\r\n" );
document.write( "4x² - 120x + 500 = 0 has roots 5 and 25\r\n" );
document.write( "10x² - 60x - 270 = 0 has roots -3 and 9\r\n" );
document.write( "5x² - 150x + 625 = 0 has roots 5 and 25\r\n" );
document.write( "4x² - 288x + 2048 = 0 has roots 8 and 64\r\n" );
document.write( "2x² - 180x - 2000 = 0 has roots -10 and 100\r\n" );
document.write( "10x² - 1100x + 10000 = 0 has roots 10 and 100\r\n" );
document.write( "8x² - 160x - 1000 = 0 has roots -5 and 25\r\n" );
document.write( "10x² - 200x + 640 = 0 has roots 4 and 16\r\n" );
document.write( "5x² - 100x - 625 = 0 has roots -5 and 25\r\n" );
document.write( "3x² - 6x + 3 = 0 has roots 1 and 1\r\n" );
document.write( "4x² - 80x - 500 = 0 has roots -5 and 25\r\n" );
document.write( "3x² - 216x + 1536 = 0 has roots 8 and 64\r\n" );
document.write( "2x² - 4x - 16 = 0 has roots -2 and 4\r\n" );
document.write( "2x² - 24x - 128 = 0 has roots -4 and 16\r\n" );
document.write( " x² - 110x + 1000 = 0 has roots 10 and 100\r\n" );
document.write( "2x² - 84x - 686 = 0 has roots -7 and 49\r\n" );
document.write( " x² - 30x + 125 = 0 has roots 5 and 25\r\n" );
document.write( "9x² - 270x - 1944 = 0 has roots -6 and 36\r\n" );
document.write( "3x² - 168x - 1536 = 0 has roots -8 and 64\r\n" );
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document.write( "There are billions of trillions more!\r\n" );
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document.write( "Edwin
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