Theme: The NRM Solver
The aim of the assignment is to give students experience in programming routine computational procedures and generate the solutions. In essence, we computerize mathematics. In this assignment, you are going to computerize generation of a root for a polynomial of order 10 using the Newton Raphson Method (NRM).
The generic ten-order polynomial is in form of
P(x) = a0 + a1x + a2x2 + a3x3+ ... + a10x10
ai is any integer.
The NRM uses the formula xn+1 = xn – p (xn)/p’(xn). p’(x) is the first derivative of p(x). The user chooses the first estimate x0 and the subsequent estimates x1, x2, …. Are generated. The iterations continue until the difference between the two successive estimates is less than the acceptable error margin or the so many iterations have been made.
You are required to develop a program that solves a ten order polynomial using the NRM. The program should prompt the user input the coefficients and a0, a1 and a10 should be non zero. The program should use the first estimate to be 1.5, the acceptable error margin should be taken to be 0.00000001 and the iterations should be considered to be too many if they exceed 70.