Algorithm 1: Design the Newton's algorithm to determine the roots of the following non-linear equation (x-2) + 4x - 8 = 0 when x is in the range [0,4]. The output of the algorithm should be a table that presents the following values k, xk, f(xk), f'(xk) and hk. For your algorithm, use a convergence tolerance of le-5. Algorithm 2: Design the Newton's method to determine the solution for the following system of equations x + 2x 2 = 0 x2 + 4x2-4 = 0 - Use a tolerance of le-4 in your algorithm. The algorithm should print the k, [xx] in each iteration in a tabular format. Note: 1. The algorithms must work for a general equation(s). 2. You cannot use a built-in function to calculate either of the algorithms. 3. The program should print the tables in the two algorithms. To pass this assessment, you must: 1. Include the complete code for the algorithms. 2. The functioning of the algorithm is illustrated by applying it to the above problems. 3. Obtain the correct final solution. Acti Go to