Question

Using Newton’s method, find the root between 0 and 1 of x^3 = 6x – 4 correct to 3 decimal places.

Answer 1

Answer:

Consider the task of finding the solutions of f(x)=0. If f is the first-degree polynomial f(x)=ax+b, then the solution of f(x)=0 is given by the formula x=-\frac{b}{a}. If f is the second-degree polynomial f(x)=a{x}^{2}+bx+c, the solutions of f(x)=0 can be found by using the quadratic formula. However, for polynomials of degree 3 or more, finding roots of f becomes more complicated. Although formulas exist for third- and fourth-degree polynomials, they are quite complicated. Also, if f is a polynomial of degree 5 or greater, it is known that no such formulas exist. For example, consider the function