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a) Find the interval of unit length that contains the smallest positive root of the equation f(x) = x^3 −5x^2 +1 = 0. Starting with this interval, find an interval of length 0.05 or less that contains the root, by Bisection method. b) Taking the endpoints of the last interval obtained in part a) above as the initial approximations, perform two iterations of the secant method to approximate the root. c) Determine the maximum error in quadratic interpolation at equispaced points.
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