SOLUTION: x^4-4x^3-4x^2+16x-32=0 this problem is really stumping me

Question 197352: x^4-4x^3-4x^2+16x-32=0
this problem is really stumping me
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

And with good reason. Using the Rational Zero Theorem, the potential rational zeros of your equation are:

I used an Excel spreadsheet to perform synthetic division on all 12 potential zeros and none of them worked. That means you either have 4 real/irrational zeros, 2 real/irrational and 2 complex, or 4 complex zeros. Using a graphing program I determined that it is the 2 and 2 situation.

The only way to solve this puppy is to use the general solution of the quartic equation. Of course, that is a computational horror that I wouldn't wish on anybody -- even if I didn't like them very well. Furthermore, I'm not going to attempt it here.

If you are really interested, go to http://en.wikipedia.org/wiki/Quartic_equation

Scroll down to 'Summary of Ferrari's Method' and then follow the steps outlined. And good luck to you. By the way,

so this one is as difficult as it gets.

John

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