I'm given a quartic function to sketch, and one of the things to find is the zeros/x-roots/x-intercepts. After a lot of guessing (and no success) I pulled it up on my trusty TI, to find the roots are all decimals. Is there a way (perhaps similar to the quadratic formula) to find the roots for a quartic? Thanks.
-For reference, the one I have is $f(x) = x^4 - 8x^2 - 7$
The equation $x^4-8x^2-7=0$ is a quadratic equation in $x^2$. Let $y=x^2$ and solve the equation $y^2-8y-7=0$, using the Quadratic Formula. Now that we know $x^2$, we know $x$.
Remark: There is a formula for the roots of a general quartic, due originally to Ferrari. A number of other mathematicians, including Descartes, produced variants. It is not computationally useful.