Please show all work when answering this question. Question 1 Consider the equation r4 - 2x³ + 2x² − 3x + 1 = 0.(a) Is there a solution on [0, 1]?(b) In order to find the solution on [0, 1] using Bisection Method, estimate howmany iterations will be needed.

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Answered: Question 1 Consider the equation x² −…

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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Step 1: Existence of the solution:

$L e t space f left parenthesis x right parenthesis equals x to the power of 4 minus 2 x cubed plus 2 x squared minus 3 x plus 1 equals 0 N o w comma space f left parenthesis 0 right parenthesis equals 1 space a n d space f left parenthesis 1 right parenthesis equals negative 1. A s comma space f left parenthesis 0 right parenthesis. f left parenthesis 1 right parenthesis less than 0 comma space there exists x element of left parenthesis 0 comma 1 right parenthesis space s u c h space t h a t space f left parenthesis x right parenthesis equals 0. H e n c e comma space t h e r e space i s space a space s o l u t i o n space o n space left square bracket 0 comma 1 right square bracket.$