Roots of a polynomial (simple)

[camilus]

$$x^3-7x^2-10x-8 = 0$$

what are the roots?? Sorry, I am horrible at doing these kinds of things, this is for another problem in my differential equations thread.

Find the general solution of the Cauchy-Euler equation Assume x>0.

$$x^3{d^3y \over dx^3} - 4x^2{d^2y \over dx^2} + 8x{dy \over dx} - 8y = 4ln(x)$$

Its been so long since I did simple roots of a polynomial, I forgot how to do it LOL! and please, this homework is due tomorrow morning, so if you can help please spare the lesson until tomorrow afternoon. I need this done by tonight, preferably right now. Thanks!

 

[epkid08]

Use p/q method to factor.

 

[camilus]

elaborate please! I haven't done simple algebra like this in like 2-3 years!

I was thinking synthetic division. Would that work?

 

[camilus]

Jesus Christ! I had the wrong polynomial!

this is the right one.

$$x^3-7x^2+6x-8 = 0$$

 

[rock.freak667]

You'd probably need to look for that formula to find the roots of a cubic polynomial since I believe that doesn't have rational roots.

 

[camilus]

yeah, 2 roots are imaginary, and 1 root is real.

The three roots are according to my calculator, 6.244297529863042, 0.37785123506847906 + i* 1.06695706407035, and 0.37785123506847906 - i* 1.06695706407035.

But there's got to be a nicer way of writing that...

 

[rock.freak667]

Check here and see if you can write it in a better way.