Find the indicated root of the given quadratic equation by finding x from Newton's method Compare this root with that obtained by using the quadratic formula2x²-5x-1=0.[2,3](3)The solution obtained by using Newton's method is approximately(Round the final answer to four decimal places as needed Round all intermediate values to seven decimal places as needed)

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Answered: Find the indicated root of the given…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Using the half interval method find one of the roots of the following equation
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1) Use Cardano's method to find the one real root of the following cubic: 3 2 x + 3x + 6x+2=0 You may leave the answer in terms of radicals. (Make sure that your answer is in terms of the variable, x.)
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ex¹ + 3x₂ = 16,4 x₁ + 3√x₂ = 7,2 Find an even (x₁, x₂) root of the set of equations using the Newton-Raphson Method. *Please give a legible and correct answer. Thank you for your help.
8) Use Newton's method to derive the ancient and long standing divide and average method for finding square roots by hand. It is also known as the Babylonian method. √r can be approximated by iterating X¡ +1² (x₁+1=1) using an initial guess x₁. Because √ is the positive solution to the equation x² - r = 0, derive the iterating formula above by simplifying the Newton's method formula using f(x)=x²-r. Note that since r is a constant, d/dx(r) = 0. 9) Use the divide and average method derived in Exercise 8 and modify your code from Exercise 5 (three times) to calculate the square roots of the following numbers to within 8 decimal places (a) r = 2 (b) r = 3 (c) r = 5 You do not need to include all of the code for these problems in the HW you turn in, as most of it will just be the same as number 5. However, write down the first 5 to 8 lines (depending on the language used) that define the function used, the initial guess, and the tolerance, along with the roots found in the end.

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Find the indicated root of the given quadratic equation by finding x3 from Newton's method Compare this root with that obtained by using the quadratic formula 2x²-5x-1=0 [2,3] The solution obtained by using Newton's method is approximately RECEN mediate values to seven decimal places as needed)