Sir Isaac Newton was one of the greatest physicists and mathematicians to ever walk the planet earth. He is known for formulating the three laws of motion known as "Newton's laws of motion", as well as the inventor of calculus, etc. Joseph Raphson was one of the greatest mathematicians known for the Raphson method, published in 1690. Isaac Newton appeared to have developed an identical formula known as Newton's method which he wrote in 1671 but this method could not be published until 1736, about 50 years after Raphson's analysis. Since they both developed their method independently, the method is now known as the Newton-Raphson method. Problem Statement The Newton-Raphson method is useful when it comes to approximating the root or roots of an equation. For a normal quadratic equation there is a well-known formula for finding the roots. There is a formula for finding the roots of a 3rd and 4th degree equation but it can be difficult to find those roots, but if the function f is a 5th degree polynomial there is no formula that can allow us to find the root...