What are the solutions to this problem? Thanks! PROBLEM #2 (9 points): Given the

Question

What are the solutions to this problem? Thanks!

PROBLEM #2 (9 points): Given the function f (x) x4 x2... PART A: List all the roots of f (x). PART B Use Bisection Method to find all possible roots of f x). Give the left and right endpoint you'd use to converge to each root. If Bisection Method cannot be used to obtain a root, explain why PART C: Use Newton's Method to find all possible roots of f x). Give the initial guess you'd use to converge to each root. If Newton's Method cannot be used to obtain a root, explain why.

Explanation / Answer

A) f(x)=x^4-x^2

x^4-x^x^2=0

x^2*(x^2-1) = 0

x^2*(x+1)*(x-1) =0

so the roots are 0,1,-1

B)for bisection method consider

f(2)>0 and f(0.5)<0

f(.5+2/2) = f(1.25) >0

we have f(1.25) and f(0.5)

f(0.5+1.25/2)=f(.875) <0

we have f(1.25) & f(.875)

f(1.25/.875) = f(1) = 0 so 1 is a root ...similarly by taking -2 and -0.5 we get -1 as root

bisection method cannot find the other root 0 as the function is not continuous at 0.

because if the function is not continuous we cannot consider the values to be assumed

C)The Newton

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