How do you solve thirdgrade equations algebraicly?
For example y=(ax^3)+(bx^2)+d

How do you solve thirdgrade equations algebraicly?
For example y=(ax^3)+(bx^2)+d
Cardano’s method
The working can be very complicated and tedious – best if you have a computer program for it.
PS: Such an equation is called a thirddegree equation, not thirdgrade equation.
Dang. I was still working on addition and subtraction when I was in the third grade.
Heh!Originally Posted by Harold14370
And I thought the answer would involve Fermat's Last Theorem! Or is that for equations of degree 4 and greater?
If you're just interested in finding roots and not integer roots, then FLT won't help you at all. Furthermore, FLT only talks about a very specific set of equations.Originally Posted by sunshinewarrior
For equations of degree less than or equal to 4, you can always find the roots via arithmetic operations and root extractions (i.e., square root, cube root, etc.). However, beginning with degree 5 and continuing on forever, there exist polynomials whose roots cannot be expressed as such. For example, the family of polynomials x<sup>n</sup>x1, n ≥ 5, are such polynomials. However, this only says that there are no elementary algebraic methods of solving these polynomials. So, for example, there are analytic methods of finding roots, so not all hope is lost!
Had forgotten about integer roots, though my post was, in any case, made more lightheartedly. Thanks for that.Originally Posted by serpicojr
My lightheartedness detectors turn off when math is involved. It's just a mathematician's instinct!Originally Posted by sunshinewarrior
I could tell SunshineWarrior was being lighthearted; I just couldn’t think of a lighthearted reply to make. :POriginally Posted by serpicojr
I know, it can be difficult to be lighthearted when trying to explain certain things in maths.
Don't worry about it  we love you just the way you are. And it's just wonderful to have mathsexpert guys like you and Lizzie's elder sister and Ratty here!Originally Posted by serpicojr
couldn't you just plug the equation into your graphing calculator and just find when where the graph intercepts the x axis?
If you're going to use a calculator, you may as well use it the right way. Most graphing calculators come with a polynomial solver. Use this instead of the graphing function.
Thansk for all the posts but could anybody please tell me, if I have the function y=ax<sup>3</sup>+bx<sup>2</sup>+cx+d what solutions does it have? I know it can be solved algebraicly and this I want to learn. Please don't answer that you can factorize it in (xa)(xb)(xc) where a,b & c are roots.
I don't think any of us here know it off the top of our heads. For serious, look it up on Wikipedia:
http://en.wikipedia.org/wiki/Cubic_e...cubic_function
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