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Inggrid Audia on 29 Sep 2016
Answered: Luis Varela on 4 Oct 2016
How can I use Newton-Raphson method to determine a root of
f (x) = x5−16.05x4+88.75x3−192.0375x2+116.35x +31.6875
using an initial guess of x = 0.5825 and εs = 0.01%.
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Luis Varela on 4 Oct 2016
On Newton Raphson method, you need calculate the function f(x) and the derivate f'(x), to get the next value of x, and continue while the error is greater than desired, for example:
x = 0.5825;
e=1;
while e>0.01
fx= x^5 - 16.05*x^4 + 88.75*x^3 - 192.0375*x^2 + 116.35*x + 31.6875;
dfx= 5*x^4 - 4*16.05*x^3 + 3*88.75*x^2 - 2*192.0375*x + 116.35;
x2=x-(fx/dfx);
e=100*abs((x2-x)/x2);
x=x2;
end
At the end x will have the value of the calculated root, aprox. x=6.5

Jakub Rysanek on 3 Oct 2016
In this case I would go with
roots([1,-16.05,88.75,192.0375,116.35,31.6875])

Luis Varela on 4 Oct 2016
On Newton Raphson method, you need calculate the function f(x) and the derivate f'(x), to get the next value of x, and continue while the error is greater than desired, for example:
x = 0.5825;
e=1;
while e>0.01
fx= x^5 - 16.05*x^4 + 88.75*x^3 - 192.0375*x^2 + 116.35*x + 31.6875;
dfx= 5*x^4 - 4*16.05*x^3 + 3*88.75*x^2 - 2*192.0375*x + 116.35;
x2=x-(fx/dfx);
e=100*abs((x2-x)/x2);
x=x2;
end
At the end x will have the value of the calculated root, aprox. x=6.5