Need a little help with solving this cubic equation.
I did the rational root test and figured out that it has either 1 or 0 rational roots. Further by the descartes method, assuming the rational root would be of either of, -1, 1, -1/2, 1/2, -2, 2, or -4, or 4.
f(2) is negative and f(4) is positive so I figured the root has to be near 3. And this further leads me to think there is no rational root.
I have run out of ideas here. The method I have been following so far have been to try to get a rational root by trial and error/via synthetic division using the assumed roots in the descartes method, then you end up with a quadratic that is easy to solve.
Without the first root, its a little hard to proceed.
I looked around on the web and found the "Cubic Formula". This thing is enormous! Can you guys guide if I missed any simpler method to do this. Do I memorize this?!
Thanks for your help!