Help Notes: Use Newton's method to find all the roots of the equation correct to eight decimal places. Use Newton's method to find all the roots of the...

Wednesday, 27 March 2013

Use Newton's method to find all the roots of the equation correct to eight decimal places. Use Newton's method to find all the roots of the...

Using a
graph we get approximations for the 4 real zeros: -2.2,-1,1,3.2

Note that
$\displaystyle{f{'}}{\left({x}\right)}={6}{{x}}^{{5}}-{5}{{x}}^{{4}}-{28}{{x}}^{{3}}-{2}{x}+{1}$

Newtons method begins with a "guess",
$\displaystyle{x}_{{1}}$ , and then generates a new "guess" by $\displaystyle{x}_{{n}}={x}_{{{n}-{1}}}-\frac{{{f{{\left({x}_{{n}}\right)}}}}}{{{f{'}}{\left({x}_{{n}}\right)}}}$

(1) Let $\displaystyle{x}_{{1}}=-{2.2}$

$\displaystyle{x}_{{2}}=-{2.2}-\frac{{{1.897024}}}{{-{122.80192}}}=-{2.184552163}$

$\displaystyle{x}_{{3}}=-{2.184552163}-\frac{{.059782097192}}{{-{{115.10915551}}}}=-{2.184032812}$

$\displaystyle{x}_{{4}}=-{2.184032812}-\frac{{.0000659453474}}{{-{{114.85541759}}}}=-{2.184032238}$

Help Notes

Wednesday, 27 March 2013

Use Newton's method to find all the roots of the equation correct to eight decimal places. Use Newton's method to find all the roots of the...

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