Hello.. I'm not sure whether this should be posted under here:
What is the standard method to solve for the following equation:
$\displaystyle 4x^4-x-9=0$
without using software.
Thanks!
Follow this.
http://en.wikipedia.org/wiki/Quartic_equation
hi
Did u mean its supposed to be an $\displaystyle x^2 $ term?
In this case:
let $\displaystyle x^2 = t $
Giving us: $\displaystyle 4t^2 -t -9 = 0 $
Which can be written: $\displaystyle (t-\frac{1}{8})^{2} = \frac{145}{8} $
Solving gives: $\displaystyle t_{1} = \frac{1+\sqrt{145}}{8} $
$\displaystyle t_{2} = \frac{1-\sqrt{145}}{8} $
But we have $\displaystyle x^2 = t $, so two solutions are:
$\displaystyle \sqrt{\frac{1+\sqrt{145}}{8}} \mbox{ and } -\sqrt{\frac{1+\sqrt{145}}{8}} $
You will also get two imaginary roots, but I donīt write them out here...
Btw: If you DID mean $\displaystyle 4x^4-x-9 = 0$, Mathematica gives me a HORRIBLE answer...