@Alpha Beta
–
For Cardano's method, I'd suggest just reading up on it. It's a bunch of algebra stating how to solve the depressed cubic (no quadratic term).

There is also a general formula for the cubic (and quartic) equation, but I can honestly say that I never bothered to memorize what they are.

[LaTex edited in by peter...not sure if I preserved Tim's order's of operations correctly (lots of parentheses), so see his top section for official version]

I don't mean to be intrusive, but I edited in a LaTex attempt of your answer so that people can read it easier. If that is not what you meant, feel free to re-edit it, using my LaTex and the formatting guide for help.

There is a link to the formatting guide at the base of the window where you enter a comment. Please put all math in LaTex as it is way easier to read than teasing out terms bounded by parentheses within parentheses. LaTex is actually easier, or just as hard as typing math the ugly way, but it is still easy to bungle. Please use the edit post button and the preview function, until your math states what you mean. Cheers:)

Easy Math Editor

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boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

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## Comments

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TopNewestYou must know the product of the roots and the sum of the roots, you can also use that

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You can use rational root theorem to know if there is a rational root, or you can cyclic factorize it.

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However, there is no rational root

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how do u get this.......

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What of the following techniques do you know how to use to factorize a polynomial?

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Please Calvin,can you teach me CARDANO'S METHOD...........PLEASEEEEEE

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There is also a general formula for the cubic (and quartic) equation, but I can honestly say that I never bothered to memorize what they are.

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1,2,3,4,5

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i want full solution please/........

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hmmm,,, i'd leave the question if i were you

anyways, you can see solutions here

Click on exact form (its dirty)

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x = -1/6 (1-i sqrt(3)) (27/2-(3 sqrt(69))/2)^(1/3)-((1+i sqrt(3)) (1/2 (9+sqrt(69)))^(1/3))/(2 3^(2/3))

\(x = \frac{-1}{6} (1-i \sqrt{3}) (\frac{\frac{27}{2}-(3 \sqrt{69}}{2})^\frac{1}{3}-(1+i \sqrt{3}) \frac{\frac{1}{2} (9+\sqrt{69})^\frac{1}{3}}{(23^\frac{2}{3})}\)

[LaTex edited in by peter...not sure if I preserved Tim's order's of operations correctly (lots of parentheses), so see his top section for official version]

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Hey Tim,

I don't mean to be intrusive, but I edited in a LaTex attempt of your answer so that people can read it easier. If that is not what you meant, feel free to re-edit it, using my LaTex and the formatting guide for help.

There is a link to the formatting guide at the base of the window where you enter a comment. Please put all math in LaTex as it is way easier to read than teasing out terms bounded by parentheses within parentheses. LaTex is actually easier, or just as hard as typing math the ugly way, but it is still easy to bungle. Please use the edit post button and the preview function, until your math states what you mean. Cheers:)

Log in to reply