A Nice Cubic Equation | Cubic Formula | #PolynomialEquations

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In this video, I talk about The Cubic Formula in detail.

If you need to post a picture of your solution or idea:
x^3=3x^2-6x+4
#PolynomialEquations #Polynomials
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PLAYLISTS 🎵 :

[MrGeorge]

In this case it is very easy to guess x = 1. (3 - 6 + 4) and factorize the polynomial to (x - 1)(x² - 2x + 4) = 0.

[MortezaSabzian-dbsl]

Just
x³=3x²-6x+4
Step 1 Move the variables as much as necessary to create a cube
x³-3x²+3x-1==-3x+3
Now that we have the materials for the cube, we will make it and get an factor
(x-1)³=-3(x-1)
We simplify similar factors by considering the roots
(x-1)²=-3
We take the root of both sides√
|x-1|=3i
We remove the absolute value and replace it with positive and negative signs

[djgiesz]

You can also put everything on the same side, and after checking the sum of the coefficients, you can see that it's 0, therefore x=1 is a solution, therefore x-1 is a factor. By considering that and rearranging the terms like x^3-x^2-2x^2+2x+4x-4=0 and factor every pair to get x^2(x-1)-2x(x-1)+4(x-1)=0 and then take out an x-1 to get (x-1)(x^2-2x+4)=0. After that you set each factor to 0 and solve for x by adding 1 to both sides and by using the quadratic formula.

[alextang]

x^3=3x^2-6x+4
x^3-1=3x^2-6x+3
(x-1)*(...)=3*(x-1)^2
Therefore 1 is a root. Then the other 2 roots can be easily found. 😊😊😊😊😊😊

[parthbairagade]

I think you should use synthetic division method to solve this

[roger]

I believe that for any cubic equation with real coefficients, at least one root must be real. I would roughly graph the curve to estimate the real root and then apply Newton-Raphson iteration to obtain a sufficiently accurate value. Finally use synthetic division to obtain the quadratic equation and apply its solution algorithm.

[goldfing]

You forgot the rasiert methid: using the r.r.t.
x^3 + 6x = 3x + 4
It is easy to see that x = 1 fulfills this equation, since
1 + 6 = 7 and 3 + 4 = 7, too.

[scottleung]

I used a third method, which is RRT and long division.

[bobbyheffley]

The complex roots are cube roots of -8.

[suvratvarshney]

Meanwhile indians taking just one step to get their answer within 1 mins. (i.e.- take all of them to one side get x as common from all possible ones then break 6 into 2 and 4 then after separating some of it's terms we will get the same equation.)