Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

That Cubic Formula

  1. Dec 17, 2009 #1

    Char. Limit

    User Avatar
    Gold Member

    The proof of the quadratic formula was so simple, I moved to the proof of the cubic formula with supreme confidence. And found myself awash in as and cs and cubic roots.

    Can you turn this equation into a cubic?



  2. jcsd
  3. Dec 18, 2009 #2
    Googling "proof of cubic forumla" gives this proof.
  4. Mar 25, 2010 #3
    First, the cubic equation: [tex]ax^3+bx^2+cx+d[/tex]. With [tex]x=y-\frac{a}{3}[/tex], you can reduce the equation to [tex]y^3+py+q[/tex]. [tex]p=b-\frac{a^2}{3}[/tex] and [tex]q=c-\frac{ab}{3}+\frac{2a^3}{27}[/tex]. In a cubic equation there are 3 possible answers, the one you listed would be one of the 3, [tex]X_{1}[/tex]
    Last edited: Mar 25, 2010
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook