Please help..you can write in pseudo code if necessary. I just can't wrap my head around this

Write a program that prompts the user to input the coefficients co, c1, c5 of a 5th-order polynomial and an initial value that serves as a the starting condition for the Newton-Raphson algorithm. The 5 order polynomial has the form We know that the first derivative of y with respect to r is dar We can use this information to find the roots of the polynomial. The basic idea, in the Newton-Raphson method, is as follows: (a) Given an initial guess r, and polynomial coefficients c, calculate y (b) Check to see if y is close enough to zero, i.e. within some small tolerance close to zero. (i) If so then terminate. Algorithm has converged! (ii) If not then continue (c) Use the current value of ar to calculate y (d) Create a new guess for r using the update formula z z- (e) Increment a counter to count the number of algorithm iterations (f) Check to see if the number of iterations has exceeded a predetermined count limit (say 500) (i) If so then terminate. Algorithm has failed! (ii) If not then return to step a This same information is described in the flow chart below