Explanation Given information: x 6 − x 5 − 6 x 4 − x 2 + x + 10 = 0 Calculation: We are given x 6 − x 5 − 6 x 4 − x 2 + x + 10 = 0 . We have to find the solution of this equation. Use Newton’s method to solve this and thus we consider f ( x ) = x 6 − x 5 − 6 x 4 − x 2 + x + 10 From the diagram it can be seen that the solutions are close to x = - 2 and x = - 2 and x = 1 and x = 3. Thus we use the Newton’s method to find the solutions with the first approximations as x = - 2 and x = - 2 and x = 1 and x = 3. We know from the Newton’s method that for a function f ( x ) and the initial approximation: x n + 1 = x n + f ( x n ) f ' ( x n ) So when we substitute x = − 2 we get: [ x 2 − 1.94666666667 x 3 − 1.93841499414 x 4 − 1.93822892796 x 5 − 1.9382288347 x 6 − 1.9382288347 ] Since we see that x 5 and x 6 both are accurate unto the 8 t h decimal digit, we can state that the one of the solution is x = - 1.93822883 So when we substitute x = − 1 we get: [ x 2 − 1

Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

1st Edition

ISBN: 9781305779037

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Chapter 3.8, Problem 27E

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To find: all the roots of x6−x5−6x4−x2+x+10=0 correct to eight decimal places using Newton’s method.

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Chapter 3.8, Problem 26E

Chapter 3.8, Problem 28E

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Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

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all the roots of x 6 − x 5 − 6 x 4 − x 2 + x + 10 = 0 correct to eight decimal places using Newton’s method.

Solution Summary: The author explains the Newton's method to find the roots of x6-xx5-6xx4-2+x+10=0.

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To find: all the roots of x6−x5−6x4−x2+x+10=0 correct to eight decimal places using Newton’s method.

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