document.write( "Question 271650: 3. By using the Newton-Raphson’s method find the positive root of the quadratic equation
\n" ); document.write( " 5x2 + 11x – 17 = 0 correct to 3 significant figures.\r
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Algebra.Com's Answer #198829 by Edwin McCravy(20056)\"\" \"About 
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3. By using the Newton-Raphson’s method find the positive root of the quadratic equation
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document.write( "    \"5x%5E2+%2B+11x+%96+17+=+0\" correct to 3 significant figures.\r\n" );
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document.write( "\"f%28x%29=5x%5E2%2B11x-17\"\r\n" );
document.write( "\"%22f%27%28x%29%22=10x%2B11\"\r\n" );
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document.write( "Choose \"x%5B1%5D=1\", \r\n" );
document.write( "\"f%28x%5B1%5D%29=f%281%29=5%281%29%5E2%2B11%281%29-17=5%2B11-17=-1\"\r\n" );
document.write( "\"%22f%27%22%28x%5B1%5D%29=%22f%27%281%29%22=10%281%29%2B11=10%2B11=21\"\r\n" );
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document.write( "\"x%5B2%5D=1.047619048\", \r\n" );
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document.write( "Checking it by the quadratic formula\r\n" );
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document.write( "\"x+=+%28-11+%2B-+sqrt%28+11%5E2-4%2A5%2A%28-17%29+%29%29%2F%282%2A5%29+\"\r\n" );
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document.write( "\"x+=+%28-11+%2B-+sqrt%28+121%2B340+%29%29%2F10+\"\r\n" );
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document.write( "\"x+=+%28-11+%2B-+sqrt%28461+%29%29%2F10+\"\r\n" );
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document.write( "Use the + to get the positive root:\r\n" );
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document.write( "\"x=1.047091055\"\r\n" );
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document.write( "So we only needed 1 iteration of the Newton-Rhaphson method\r\n" );
document.write( "to get it to three significant figures, for what we had then\r\n" );
document.write( "would have rounded to 1.05.  By taking it one more step we\r\n" );
document.write( "have it to 4 significant figures 1.047.\r\n" );
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document.write( "Edwin
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