I'm not sure how to approach this problem

For the function f(x) = x3 5.12:2 + 7.021 1.05, a young researcher was convinced that one root of this equation must be between 0 and l. (a) Based on what reason do you think this young researcher decided to do that? (b) The researcher Wishes to conduct 3 iterations of the Falseposition method to narrow down this interval. Please conduct these three iterations (by hand), using only a calculator and reporting only 3 decimal digits in each iteration (please do not use hiatlab for this you may use a IVIatlab program just to conrm that you are correct with your manualf calculator calculations). (c) The Falseposition method computations from part (b) will yield an interval that brackets the solution we are seeln'ng. Select the bound of this interval at which f(x) evaluates closer to zero and perform 4 iterations (by hand) of the fastest possible method that can bring us closer to the actual root of f(x). Please explain which method you picked and why