Hello, i dont know if its possible but can someone simply explain me how to solve a third degree equation with numerical analysis?
Well, i came across some equations in thermodynamics that was solved with this method it seemed eaiser and faster but i couldnt figure it out on my own. they actually showed us about it in calculus ii last year but i didnt pay much attention since i didnt need it untill now. theres no particular polynominal, feel free to give a simple example.
thanks.
Well as you studied calculus I would suggest using newton's method. It is an iterative process.
You keep calculating the next value until you see convergence. This value will be the solution.
For the polynomial $\displaystyle \displaystyle f(x)=x^2+2x+7$ choose a starting value in the neighbourhood of the solution, in this case $\displaystyle \displaystyle x_0=-2$ and apply $\displaystyle \displaystyle x_{n+1} =x_n-\frac{f(x_n)}{f'(x_n)}$
First find $\displaystyle \displaystyle x_1$
$\displaystyle \displaystyle x_{1} =x_0-\frac{f(x_0)}{f'(x_0)}= -2-\frac{f(-2)}{f'(-2)}$
What did you get?
Spoiler:
Note this value and find $\displaystyle \displaystyle x_2$ repeat