A Quick and Easy Cubic Equation | Algebra

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x^3-8x=8
#PolynomialEquations #Polynomials
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[farhansadik]

Loved the lamborghini method 🤣🤣 So good!

[barteqw]

It's easy to find that -2 is the root because w(-2)=(-2)^3-8*(-2)-8=0. So w(x)=x^3-8x-8=(x+2)*p(x), where, after division, one's found p(x)=x^2-2x-4. Solving quadratic equation we get discriminant = 20, and x1=1+sqrt(5), x2=1-sqrt(5).

[Chitin-qyxy]

U r so creative, smart, and active keep those behaves to ur mind I appreciate it

[leif]

Mr. Syber this cubic method only works if you have a cubic in this convenient form like depressed and the coefficents fit--otherwise you can't use this method or not this way. Thanks for sharing.

[alextang]

(-2)^3=-8
-8(-2)=16
So -2 is the root, the using long division, we get a quadratic equation and finally the other 2 roots.
In short, we can try the integer roots for 8's factors.

[Qermaq]

I just experimented with factoring and saw that if I added then subtracted 2x^2, then split the -8x into 2 of -4x, I could factor out x+2. Then it's easy.

[j.r.]

I'm trying very hard to see a genuine "formula" at work in this application of the cubic formula, but it just looks like a deliberate choice of the most tortuous mathematical path possible. :) And you even omitted several steps as an act of mercy!

[rickdesper]

Rational root theorem tells you any rational root would be a factor of -8. And hey, -2 works! Factor out (x+2) and then you have a quadratic. Finish up lickety split.

[wonghonkongjames]

GOOD MORNING SIR
Putting y=x÷2 substitute into the equation we have (y-1)*(y²+y+1)=2y
Let y=-1 then y²+y+1 should be =1
Therefore (-1)²-1+1=1
Hence x=-2
Thank you

[nmarks]

Is it possible to find the roots of any equation of order n by writing out the binomial expansion of (a+b)^n, then going from there?

[eckhardfriauf]

0:35 Lamborghini method! I assume the method was named Gina Lollobrigida method. ;-)

[MrLidless]

8s, 8s…with minimal brain power x = -2 is a solution, and the rest falls out.