Use Newton-Raphson to find a solution to the polynomial equation (f(x)=y) where (y=0) and (f(x)=x^{3}+8 x^{2}+2 x-40).

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Use Newton-Raphson to find a solution to the polynomial equation \(f(x)=y\) where \(y=0\) and \(f(x)=x^{3}+8 x^{2}+2 x-40\). Start with \(x(0)=1\) and continue until (6.2.2) is satisfied with \(\varepsilon=0.001\).

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