Suppose there is a polynomial p(x) = (x p) (x - e)(x ) where...

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Suppose there is a polynomial p(x) = (x − p) (x - e)(x − π) where is the golden ratio, e is the natural exponential base, and π is, well, π. This poly- nomial has 3 roots. a.) What will happen if you run the Bisection algorithm with initial interval [a, b] = [0, 4]? Do a few iterations of the algorithm by hand to support your conclusion. b.) Find an interval [a, b] which still contains all zeros to p(x), for which the Bisection al- gorithm would converge to x = T. Support your answer by running the Bisection algorithm and reporting the results. No code needed, just report the results and discuss to support your answer. c.) Write a MATLAB script that will use the Bisection algorithm to find all three roots to this equation by using several intervals instead of just 1. Suppose there is a polynomial p(x) = (x − p) (x - e)(x − π) where is the golden ratio, e is the natural exponential base, and π is, well, π. This poly- nomial has 3 roots. a.) What will happen if you run the Bisection algorithm with initial interval [a, b] = [0, 4]? Do a few iterations of the algorithm by hand to support your conclusion. b.) Find an interval [a, b] which still contains all zeros to p(x), for which the Bisection al- gorithm would converge to x = T. Support your answer by running the Bisection algorithm and reporting the results. No code needed, just report the results and discuss to support your answer. c.) Write a MATLAB script that will use the Bisection algorithm to find all three roots to this equation by using several intervals instead of just 1.

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a If we run the Bisection algorithm with initial interval a b 04 it will not converge to any of the three roots of the polynomial We can see this by o... View the full answer