I need some help trying to write a code for polynomial deflation by using newtons method and synthetic devsion in C/C ++ syntax for my numerical analysis class.

Lab #2: Finding all roots of a Polynomial Using Newton's Method Write a program that uses Newton's method to find ALL of the roots of a polynomial, even the complex roots. The user of the program should only enter the information that describes the polynomial : the degree of the polynomial first then the leading coefficient, on and on until finally the constant coefficient. For example, if the polynomial is 2x^5 +7x^4 - 9x^3 + 17x^2 + 30% -12 then the input will be 5 (this is the degree) 2 (this is the leading coefficient) 7 17 30 -12 (this is the constant coefficient) The program should generate its own guesses for the Newton's method algorithm. These guesses should have a non-zero imaginary part if you wish to find the complex roots... starting with a real guess will only find a real root. Once Newton's method finds its first root, use synthetic division to deflate the polynomial and then proceed to find a root of the defalted poly. Once a root is found for this deflated polynomial, deflate again and continue until all roots have been found. We recommend just running Newton's method 50 times for each root....this will probably work well enough. Synthetic division can be used not only for deflating the polynomial but also for evaluating the polynomial and it derivative. The ideal code will do this though we are tolerant of not doing so