# eigenvalues vs roots of characteristic polynomial

Hi,

Sorry if this is a stupid question but I am struggling to make Sage compute the exact eigenvalues of a matrix. I am also confused that when I ask for the roots of the characteristic polynomial Sage answers with complex roots... I am new to Sage so please forgive me :)

Here is my worksheet:

```
sage: A = matrix([[1, 1, 2], [1, -2, 0], [2, 0, 1]])
sage: A
[ 1 1 2]
[ 1 -2 0]
[ 2 0 1]
sage: A.eigenvalues()
[-2.439311671683875?, -0.6611203141265045?, 3.100431985810380?]
sage: x = var('x')
sage: H = A.charpoly()
sage: H
x^3 - 8*x - 5
sage: H.roots()
[]
sage: (x^3-8*x-5).roots()
[(-1/2*(1/18*I*sqrt(1373)*sqrt(3) + 5/2)^(1/3)*(I*sqrt(3) + 1) + 1/3*(4*I*sqrt(3) - 4)/(1/18*I*sqrt(1373)*sqrt(3) + 5/2)^(1/3),
1),
(-1/2*(1/18*I*sqrt(1373)*sqrt(3) + 5/2)^(1/3)*(-I*sqrt(3) + 1) + 1/3*(-4*I*sqrt(3) - 4)/(1/18*I*sqrt(1373)*sqrt(3) + 5/2)^(1/3),
1),
((1/18*I*sqrt(1373)*sqrt(3) + 5/2)^(1/3) + 8/3/(1/18*I*sqrt(1373)*sqrt(3) + 5/2)^(1/3),
1)]
```