solving cubic equation
Can someone tell me how to solve any cubic equation in the form ax^3+bx^2+cx+d=0? Tell me why you did the steps you did.
[header]Help[/header]
Okay people, my homework is to [i]generalize[/i] a way to solve cubic equations. Don't say factor or plug using synthetic division, because they don't necessarily work.
December 12, 2010
16 Comments • Newest first
[quote=RoyalxNub]There's the cubic formula that will always work. There you go.
Other than that you can use the location theorem, rational root theorem , synthetic division and the rest to find zeros[/quote]
How do you arrive at the cubic formula? That is the general way to solve cubic equations.
General is grouping, but sometimes it doesn't work out as not all equations can be factored to get equal groups.
EX: x^3 + x^2 + x + 1
1. Factor. x^2(x + 1) + 1(x+1)
2. Do this. (x^2 + 1) (x + 1)
3. Factor more if possible.
4. Put both equal to zero.
x^2 + 1 = 0 & x + 1 = 0
X = + or - _ and _
Hope I helped.
[quote=xfeeshie]Try grouping method if that doesn't work use synthetic.[/quote]
Do you know a general way to solve any cubic?
Try grouping method if that doesn't work use synthetic.
[quote=KingHippo]It's easy dude just complete the cube.[/quote]
AWESOME I FOUND SOMEONE THAT CAN TEACH ME. Please teach me how to do this!
@radkai:
Fail, just fail.
Sorry, I really do suck at math. = =
[quote=Shrimp]I can has factor by grouping?[/quote]
I want a method of solving cubics that will always work. The method for quadratic that will always work is complete the square.
[quote=cutie]LOL OMG, I just remembered how to do these... - -
Use synthetic division.
The root for the problem: x^3+2x^2+x+1=0 is x=-1 btw.[/quote]
Synthetic division is for dividing polynomials. The solution to that random equation I wrote isn't -1.
LOL OMG, I just remembered how to do these... - -
Use synthetic division. (Please tell me you know how to do that D:<<
The root for the problem: x^3+2x^2+x+1=0 is x=-1 btw.
[quote=cutie]When there are complex roots, you leave it as it is. Ex: 2i sqrt. 5
To be honest, I use the calculator for these types of problems. x_x[/quote]
It's not that. I have to write how to arrive at the cubic formula and the basic thing I have to know is to solve any cubic equation.
@UnShuffle I didn't ask how to solve quadratic equations.
[quote=radkai]There can be complex roots.[/quote]
When there are complex roots, you leave it as it is. Ex: 2i sqrt. 5
To be honest, I use the calculator for these types of problems. x_x
[quote=darksuitguy]Factors of d/factors of a=all possible solutions.
Just plug and chug until you get one right. Then factor the remaining quad function.[/quote]
There can be complex roots.
@ikickazzxd grouping isn't a reliable way to solve cubics.
Solve it by grouping them
Factors of d/factors of a=all possible solutions.
Just plug and chug until you get one right. Then factor the remaining quad function.
[quote=cutie]Solve that equation for what variable?
Do you have an example problem?[/quote]
x^3+2x^2+x+1=0 just an example I made on the spot
Solve that equation for what variable?
Do you have an example problem?