Math Is Fun Forum

katoroh

Member

Registered: 2020-01-03

Posts: 1

Solutions to Cubic Equations (third degree)

Hi! Does anyone know how to find solutions to polynomials of third degree that can be irrational or not whole numbers? I'm studying for a math competition on which I cannot use a calculator or anything of that sort, and since there is a limited amount of time, I would not like to use plug-and-chug. This is like for those were rational roots theorem  does nothing, and Newton-Raphson is too complicated without a CPU. Thank y'all so much !!!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Solutions to Cubic Equations (third degree)

hi katoroh

Welcome to the forum.

There is a formula for this but I don't think it will help in a test situation:

https://math.vanderbilt.edu/schectex/courses/cubic/

There are some helpful tips here:

https://www.wikihow.com/Solve-a-Cubic-Equation

If you are doing a math competition, then the questioners are looking for clever applications of math not number crunching.  All cubics must have at least one real solution and, once found, the remaining quadratic can be solved with the formula.  So the person making up the question should be giving you such a route into the problem.  Most likely you may be able to spot a factor using the factor theorem

https://www.mathsisfun.com/algebra/poly … actor.html

Have you got any 'past papers' with such questions?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Re: Solutions to Cubic Equations (third degree)

The method in this proof might help: https://proofwiki.org/wiki/Cardano%27s_Formula

The key is to annihilate the square term first...

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.