This problem concerns the computer implementation of Newton's method for finding the real roots (zeros) of a function f(x) of a single variable. Develop the steps in an algorithm to implement Newton's method of finding the real roots of f(x) = 0. You may assume that a function is available to calculate the value of the desired function f(x) and f'(x) at x. Your algorithm should provide appropriate error and convergence checks. (You may use C/C+ syntax to describe the algorithm.) Discuss the main advantages of Newton's method. Discuss the main disadvantages of Newton's method are. In calculating the value of a polynomial function f(x) = a_nx^n + a_n-1 x^n-1 + + a_0 in C++ it is unwieldy to repeatedly calculate x^j. Develop an alternative formulation for calculating the polynomial expression that avoids the need for repeated power calculation and reduces the risk of numerical instability. (You may describe your formulation using C/C++ syntax if you wish.)