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 equation correct to eight decimal places. Start by...

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 equation correct to eight decimal places. Start by drawing a graph to find initial approximations. (Enter your answers as a comma-separated list.)

 

x6 − x5 − 7x4 − x2 + x + 8 = 0

x=_____________________?

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

Note that `f'(x)=6x^5-5x^4-28x^3-2x+1`

Newtons method begins with a "guess", `x_1` , and then generates a new "guess" by `x_n=x_(n-1)-(f(x_n))/(f'(x_n))`

(1) Let `x_1=-2.2`

`x_2=-2.2-(1.897024)/(-122.80192)=-2.184552163`

`x_3=-2.184552163-.059782097192/-115.10915551=-2.184032812`

`x_4=-2.184032812-.0000659453474/-114.85541759=-2.184032238`

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