(a) Using Newton's Method by hand, approximate s=(415)1/8 correctly to within eight decimal places. Use a calculator to assist you. Hint: To start find a polynomial with s as a zero. Use an initial guess of x1=2. Show all your work. (b) Implement Newton's Method in Python using code that you write yourself. You may use whatever stopping criterion* you like that will allow you to answer the following problems. So your program may accept a number of iteration steps or a tolerance as an input. " Stopping criteria: Many iterative methods will not reach the solutions exactly, so we need to provide some instruction on when the iterations should stop. Two ways this can be by putting an upper limit on the total number of iterations or by stopping when a value has become less than a specified tolerance. (c) Using your Newton's Method code from part (b), find the roots of g(x)=x2+5x6. What did you choose for your initial guess? (d) Check your answer from part (a) using your code from part (b)