SOLUTION: 3. By using the Newton-Raphson’s method find the positive root of the quadratic equation 5x2 + 11x – 17 = 0 correct to 3 significant figures.

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Question 271650: 3. By using the Newton-Raphson’s method find the positive root of the quadratic equation
5x2 + 11x – 17 = 0 correct to 3 significant figures.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
3. By using the Newton-Raphson’s method find the positive root of the quadratic equation 

    5x%5E2+%2B+11x+%96+17+=+0 correct to 3 significant figures.

f%28x%29=5x%5E2%2B11x-17
%22f%27%28x%29%22=10x%2B11

Choose x%5B1%5D=1, 
f%28x%5B1%5D%29=f%281%29=5%281%29%5E2%2B11%281%29-17=5%2B11-17=-1
%22f%27%22%28x%5B1%5D%29=%22f%27%281%29%22=10%281%29%2B11=10%2B11=21




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x%5B2%5D=1.047619048, 






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Checking it by the quadratic formula

x+=+%28-11+%2B-+sqrt%28+11%5E2-4%2A5%2A%28-17%29+%29%29%2F%282%2A5%29+

x+=+%28-11+%2B-+sqrt%28+121%2B340+%29%29%2F10+

x+=+%28-11+%2B-+sqrt%28461+%29%29%2F10+

Use the + to get the positive root:

x=1.047091055

So we only needed 1 iteration of the Newton-Rhaphson method
to get it to three significant figures, for what we had then
would have rounded to 1.05.  By taking it one more step we
have it to 4 significant figures 1.047.

Edwin