Finding the Zeros

[DaMoose19]

Hi, I need help find the REAL zeros for the equation:
G(x)=x^4+8x^3+8x^2-52x-105
I've tried synthetically dividing all of the possible roots which are 1,105,3,35,5,21,7,and 15 and none of them came out to 0. I've also noticed that the equation doesn't factor. I am confused at how to go about solving this problem.

Any help would be greatly appreciated.

 

[galactus]

This one does not factor nice because it has 2 complex roots and two reals. The real roots are not integers.

One of the best ways to find the roots may be the Intermediate Value theorem.

Try a guess at a root and see if we get closer and closer to 0.

Try x=2.6 and see how close that gets. Then, try -5.4 and try honing in on that one.

The complex roots. There are two. Once you find one, the other is the conjugate.

One is -2.5972+.8538i, out to 4 decimal places

I would use some sort of technology to find the roots. Graph it and see where it crosses the x-axis. Of course two roots are complex so those will not cross the x-axis.