Questions tagged [cubics]
This tag is for questions relating to cubic equations, these are polynomials with $~3^{rd}~$ power terms as the highest order terms.
1,360
questions
2
votes
4
answers
250
views
Solving $a = b^2 + 2b^2(1 - b)$ for $b$
My algebra is very rusty, it's been about 15years since I studied, and I was stumped recently when trying to rearrange this formula;
$$a = b^2 + 2b^2(1 - b)$$
to give $b$ in terms of $a$.
Can ...
- 81
2
votes
1
answer
2k
views
Generic way to factor cubic equations?
I have a cubic equation:
$$-x^3 + 7x^2 - 16x + 12 = 0.$$
How they showed us to solve this quickly is to simplify the equation to
$$-(x - 2)^2 (x - 3) = 0$$
and find the solutions this way.
My ...
- 431
27
votes
1
answer
23k
views
Using Vieta's theorem for cubic equations to derive the cubic discriminant
Background:
Vieta's Theorem for cubic equations says that if a cubic equation $x^3 + px^2 + qx + r = 0$ has three different roots $x_1, x_2, x_3$, then
$$\begin{eqnarray*}
-p &=& x_1 + x_2 +...
- 2,037
4
votes
4
answers
7k
views
Factoring cubic polynomial
Trying to figure this one out but I see no logical approach to this at all.
$$x^3-3x^2-4x+12$$
I know that it will be 3 parts most likely and that each will start with x but beyond that I will just ...
user138246
2
votes
3
answers
1k
views
Find the root for a third degree polynomial?
So far in this course we have not been given any formula for solving third degrees polynomials.$$\frac{1}{3}x^3-2x^2+4x$$
I was thinking about doing it like this
$$x(\frac{1}{3}x^2-2x+4).$$
But that ...
- 1,909
5
votes
3
answers
7k
views
Finding the real root of a cubic algebraically
I'm sorry if this is a very easy question but my brain is fried tonight and I can't think how to do it.
I need to solve $x^3 = 2 - x$.
Obviously by eyeballing the equation you can see that the only ...
user17184
9
votes
3
answers
15k
views
Is there a systematic way of solving cubic equations?
According to my text book, to solve cubic equations, I need to
By trial & error find what value $a$ will make the cubic $0$. The factor will be $(x-a)$.
Then the other factor will be $Ax^2+Bx+C$ ...
- 4,603
8
votes
2
answers
7k
views
Fast and robust root of a cubic polynomial with constraints
I'm looking for a fast and robust method for finding a root of a cubic polynomial
$$x^3 + px^2 + qx + r$$
To make the search more robust and faster, I'd like to leverage these properties:
The ...
- 97
5
votes
1
answer
2k
views
Solving a real cubic using trigonometric methods
The problem is to figure out how to solve a real cubic equation of the form $x^3 + px + q = 0$ using trigonometry. The first step is to prove the identity
$$
4\cos^3 \theta - 3\cos \theta - \cos ...
- 561
4
votes
1
answer
725
views
How may I solve this Cubic Equation?
How can I solve this cubic equation?
$$H^{3} − 3\left[(1 + A\cos(T) )^{2} + \frac{2r \cdot A \sin(T)}{B}\right]H + 2(1 + A \cos(T))^{3} = 0$$
Solution in terms of H.
Edited in order to give more ...
- 393