How to solve cubic polynomials.

How to solve cubic polynomials. Learn this trick. #mathcompetition #maths #polynomials #cubicequation #cubicpolynomials

[@carultch]

Part of the Cubic formula's history, was Tartaglia presenting it as a poem to Cardano. I came up with a poem of my own for the cubic formula. Enjoy. x^3 + n*x = m x = cbrt(m/2 + sqrt(D)) + cbrt(m/2 - sqrt(D)) D = (m/2)^2 + (n/3)^3 When x is cubed and x times n, Are added and equal to m. The values of x, The goals of our quest, Here's how to calculate them. Cube roots to add, Square roots they had, Both of a term we'll call D. Square half of m, Cube third of n, Add together and see. Half of m, adds to the root, First with a sign of plus. Its little brother, Is just like the other, Except with a sign of minus. Cube rooting time, of both the brothers, Add up the roots with glee. We found our first x, But where is the next? I know there have to be three. With help from DeMoivre, Who's theorem, we love ya, There's cube roots all over the plane Yes, they're complex, But do not perplex, A new kind of numbers we gain.

[@JJONLINEMATHSCLASSchannel]

Wow! I love this. Thanks

[@ndivhuwomaseko6232]

Am going to be a mathematician becz of you mam 😂 thanks to u too

[@JJONLINEMATHSCLASSchannel]

Most welcome 😊

[@user-dq3uh6ee5w]

-1, 5.

[@Amos_Ruto]

I really love your videos. May i know where you teach.

[@JJONLINEMATHSCLASSchannel]

U are welcome. I teach online

[@victoryinthescriptures4440]

Question. As you were solving and got -4x squared - 9x - 5. Right under its -4x squared -4x. When calculating wouldn't -9x and -4x be -13x. Two negatives add up together or am I not seeing it correctly.

[@carultch]

I prefer doing it with synthetic division. The way it works, is you write the root in question, out in front. Then you write each coefficient inside the upside down "division house". Keep a row clear, and then bring down the first coefficient, and multiply by the root being tested. Write the result below the 2nd coefficient. Add up each column, and repeat with each result as the "seed" to your next multiplication. For this example, x=-1 is the root under test, and x^3 - 3*x^2 - 9*x - 5 = 0 is the original polynomial. This means we populate the following synthetic division structure: -1 | _ 1 _ _ -3 _ _ -9 _ _ -5 _ _ _ _ _ _ -1_ _ _+4 _ _ +5 _ _ _ 1 _ _ -4 _ _ -5 _ _ _ 0 Since the final number came out to zero, this means we have a hit on the root under test and no remainder. Thus, the factored form in progress is: (x + 1)*(x^2 - 4*x - 5) = 0 From there on out, it's just a quadratic formula to solve the rest. The addition you asked about is what happened when -1*-4 is added to -9. Since a negative times a negative is a positive, we get -9 + 4, which adds up to -5.

[@JJONLINEMATHSCLASSchannel]

-9x -(-4x) is the samething as -9x+4x which is -5x

[@JJONLINEMATHSCLASSchannel]

Thanks so much for this. I appreciate

[@victoryinthescriptures4440]

@@JJONLINEMATHSCLASSchannel yes. I saw my mistake later on. Thank you. :)

[@glasssmirror2314]

I hate trial an error in maths.

[@JJONLINEMATHSCLASSchannel]

In some cases, you don't have any other option. So it's a must in some cases