1. ## solving cubic functions

What technique is used to find zeros (real and complex) for something like:
f(x) = x³ - 3x² + 12
I know from discriminant that is has two complex roots, and I can estimate real root from graph, but don't know, algebraically, how to find exact answers.

Thanks for any help.

2. $\frac{p}{q}$ and synthetic division.

Descartes Rule of Sign to determine possibilities

3. There is a "cubic equation", its a bit nasty but for this particular function could be worth a look.

The "Cubic Formula"

4. in this case, I know the real root to be:
1 - 1/(∛(5 - 2√(6)) - ∛(5 - 2√(6))

I'm having trouble envisioning these techniques getting me there

5. Originally Posted by Jim Pfoss
in this case, I know the real root to be:
1 - 1/(∛(5 - 2√(6)) - ∛(5 - 2√(6))

I'm having trouble envisioning these techniques getting me there
Messy but divide out the real linear factor leaving you with a quadratic, then use the quadratic formula to get the complex roots.

I would not do this by hand myself as that is too error prone, but would use a symbolic mathematics system (Maxima, of Wolfram Alpha are two obvious candidates)

CB

6. Originally Posted by Jim Pfoss
in this case, I know the real root to be:
1 - 1/(∛(5 - 2√(6)) - ∛(5 - 2√(6))

I'm having trouble envisioning these techniques getting me there
Hi again, how did you get this answer? which method did you use?

7. The solution is from an automated solver site. It agrees with graphic estimation. I know it's a sin, but, hey, I'm a sinner.
If I knew the strategy to find a real root, I can do the math to find other real or complex roots, but I'm stuck on square one.

8. Originally Posted by Jim Pfoss
I know it's a sin, but, hey, I'm a sinner.
Well at least your not in denial, I respect this!

Have a read of this, it gives you a step by step to how to solve a cubic.

The "Cubic Formula"

9. Ahhh...
I'm a believer.
Thanks.