How can I solve a generic third degree equation?

Answer 1

Using numerical methods like Bisection Method/ Secant Method or using the fastest of all, Newton Raphson method.

Newton Raphson method requires you to find the derivative of the function.

The formula is as below:

x_n+1=x_n - f(x_n)/f^'(x_n)

Steps to solve:

1. Find derivative of f(x) that is f’(x)
2. 1st value of Xn say X0 is an assumed value. Value can be assumed by calculating value of function between 2 numbers such that the value of function has opposite signs. For eg assumed 2 numbers a and b. Find f(a) and f(b). If they have opposite signs then your root lies between a and b. Thus choose any value of X0 between a and b.
3. Find f(X0) and f’(X0).
4. Find X1 using formula mentioned above.
5. Find % difference between X0 and X1. If it is less than 5% X1 is your answer. If not, find f(X1) and f’(X1). Find X2 using above formula. Calculate % change between X1 and X2. If less than 5%, then X2 is your answer, if not repeat step 5.