1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Cubic equation

  1. Sep 28, 2008 #1
    Find the roots of the equation
    x^3 - 3x^2 - 10x +24 = 0

    I personally, have never done cubic equations so can you please explain what should i do here. Should i try with GCF, even though i dont see one yet, or is there a method to do this?
  2. jcsd
  3. Sep 28, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    You're going to have to factor it. There's a method, thanks to the rational root theorem (look it up, ok?) the only possible rational roots of that equation are the divisors of 24 (plus and minus). And if c is a root, then (x-c) is a factor. Divide that factor out and look for another one.
  4. Sep 28, 2008 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    The "rational root theorem" that Dick referred to says that if the fraction (rational number) m/n is root of a polynomial equation axn+ bxn-1+...+ yx+ z= 0, with coefficients a, b, c, ..., y, z integers, then n must evenly divide a and m must evenly divide z. Here a= 1 and only 1 and -1 evenly divide that. z= 24 and [itex]\pm 1[/itex], [itex]\pm 2[/itex], [itex]\pm 3[/itex], [itex]\pm 4[/itex], [itex]\pm 6[/itex], [itex]\pm 8[/itex], [itex]\pm 12[/itex], and [itex]\pm 24[/itex] evenly divide that. That means that the only possible rational roots are [itex]\pm 1[/itex], [itex]\pm 2[/itex], [itex]\pm 3[/itex], [itex]\pm 4[/itex], [itex]\pm 6[/itex], [itex]\pm 8[/itex], [itex]\pm 12[/itex], and [itex]\pm 24[/itex]. Plug them in and see if any of those satisfy the equation. If one does, then you can divide by x- that root to get a quadratic equation solved by the other 2 roots. Of course it is possible that none of them satisfy the equation: that there are no rational roots. In that case, there is a "cubic formula" but it is much more complicated than the quadratic formula and you really don't want to have to do that!
  5. Sep 28, 2008 #4
    Ok so for the first root, by method of trial and error, i got x = 4. I divided the polynomial with x-4, received a quadratic equation and got x2 = -3 and x3 = 2.
    I think it's correct, so thank you :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Cubic equation
  1. Cubic equation (Replies: 5)