(Solved): (25pts) The Bisection method (a) Using the bisection method, find a zero of the following function ...

(25pts) The Bisection method (a) Using the bisection method, find a zero of the following functions with an accuracy within \( 10^{-1} \) : i. \( x^{4}-2 x^{3}-4 x^{2}+4 x+4=0, \quad x \in[-2,-1] \) ii. \( e^{x}=4 x, \quad x \in[0,1] \) (b) Let \( f(x)=(x+2)(x+1) x(x-1)^{3}(x-2) \). To which zero of \( f \) does the Bisection method converge wen applied on the following intervals? i. \( [-3,2.5] \) ii. \( [-2.5,3] \) iii. \( [-1.75,1.5] \) (c) Let us consider a function \( f \) which has only one zero in the interval \( [-2,7] \). How many iteration \( n \) are needed to approximate the zero within \( 10^{-5} \) ?