Question

Solve: x^4+x^3-14x-12=0

Answer 1

I don't think either of you suggestions are roots... just using the factor theorem

f(-3) = 81 - 27 + 42 - 12

f(-2) = 16 - 8 + 28 - 12

neither equals zero...

Answer 2

There are two real roots. Refer to the attached plot.
{ x = -0.863422 }, { x = 2.37565 }

Answer 3

How did you find that? I'm confused on the process so if you could explain that would be really helpful!

Answer 4

I use Mathematica 8 Home Edition for calculating problems on this site.
One of the Mathematica functions, NSolve, will provide the numeric solutions shown below.\[\text{NSolve}[x{}^{\wedge}4+x{}^{\wedge}3-14x-12\text{==}0,x]
\]{{x->-1.25611-2.06699 I},
{x->-1.25611+2.06699 I},{x -> -0.863422}, {x -> 2.37565}}

The two symbolic real solutions are attached as a tiff file. This site's LaTex system appears unable to cope with the solution complexities.