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1. a) A negative root of smallest magnitude of the equation x 5x 20 0 3 + + = is to be determined i) Find an interval of unit length which contains this root ii) Perform two iterations of the bisection method iii) Taking the end points of the last interval as initial approximations perform one iteration of the secant method. (5) b) Find a root of the equation 0 3x 10x 10x 7 3 2 + + + = which is close to − 0.2 using the Birge-Vieta method. Perform two iterations of the method. (3) c) Obtain the cube root of 12 using Newton-Raphson formula.
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