Math Help - Numerical analysis

1. Numerical analysis

Hello, i dont know if its possible but can someone simply explain me how to solve a third degree equation with numerical analysis?

2. Are you looking to find the roots of a third degree polynomial with a numerical method?

3. Yes.

4. Ok, what methods have you been taught or is this independent learning (happy to suggest some methods), either is fine, do you have a polynomial in particular that needs solving?

5. 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.

6. 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 $\displaystyle f(x)=x^2+2x+7$ choose a starting value in the neighbourhood of the solution, in this case $\displaystyle x_0=-2$ and apply $\displaystyle x_{n+1} =x_n-\frac{f(x_n)}{f'(x_n)}$

First find $\displaystyle x_1$

$\displaystyle x_{1} =x_0-\frac{f(x_0)}{f'(x_0)}= -2-\frac{f(-2)}{f'(-2)}$

What did you get?

Spoiler:
$\displaystyle x_{1} =-2-\frac{7}{8}=-2.875$

Note this value and find $\displaystyle x_2$ repeat

7. Thank you.