Plot this polynomial in the interval -100 100 find the

Question

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).