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To solve using Newton's method apply the formula,
Plug in f(x) and f'(x) in the formula,
See the attached graph to get the initial values of x.
When f(x)=0 , the values of x are near The curve has three x values x `~~` 0.8 , -1.8 , -3.6
Use these three values for finding the roots of the equation to six decimal places.
Let's solve for the first zero by initial value x_1=0.8
Let's stop iteration as we have same decimal places
Now let's solve for the second zero by initial value x_1=-1.8,
Now let's solve for the third root by initial value x_1=-3.6
Roots of the equation to six decimal places are 0.889470 , -1.862365 , -3.637958
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