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In the following polynomial d is the last two digits of your student ID. For example if your ID is 207005123 then d = 23 or if your ID is 207005102 then d = 2.
x3 - 300x2 + (10000 - d2)x + (100d2 - 20000d + 1000000)
(a) Plot this polynomial in the interval [-100, 100]. Find the number of roots, and their approximate locations in this interval (Include this plot).
(b) Try following algorithms to find the root with an error tolerance of 0.5%
i) Bisection method
ii) Newton-Raphson method
iii) Secant method
for Each algorithm, provide the results: including your initial guesses, the number of iterations until convergence if applicable for each method used. Try to summarize your results in a Table).
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.With the conditions of problem 1, if 20 students are selected , what is the probability that the mean of their scores is greater than 18?
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