Roots of 3rd degree polynomials and Characteristic Polynomials
I am in desperate need of some algebra help! I'm working with matrices and diagonalization. One step of this is finding the C(x) (characteristic polynomial) which entails find the determinant of a matrix with x's along its diagonal. So this is the matrix I have:
x-3 0 7
0 x-5 0
-7 0 x-3
For the determinant I get: x^3 - 11x^2 +88x -290
To continue, I need to find the roots of this, and I have no clue how to do that. I put the matrix in here so that if I made any mistakes with the determinant you can let me know. Your help would be much appreciated! I have an exam tomorrow and I'm quite a bit behind with studying... :( Just please, if you can, answer in really simple terms, because I am pretty new at this.