`x^6 - x^5 - 6x^4 - x^2 + x + 10 = 0` Use Newton's method to find all roots of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.

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Chapter 4, 4.8 - Problem 23 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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See the attached graph. From the graph the roots of f are approximately -1.9 , -1.2 , 1.1 and 3.

Approximate until the eight decimal places are same.

For x_1=-1.9







Now for x_1=-1.2





Now for x_1=1.1






Now for x_1=3






To eight decimal places the roots of the equation are,

-1.93822883 , -1.21997997 , 1.13929375 , 2.98984102

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