Root[f, k] is automatically reduced so that f has the smallest possible degree and smallest integer coefficients.
The ordering used by Root[f, k] takes real roots to come before complex ones, and takes complex conjugate pairs of roots to be adjacent.
The coefficients in the polynomial f[x] can involve symbolic parameters.
For linear and quadratic polynomials f[x], Root[f, k] is automatically reduced to explicit rational or radical form.
For other polynomials, ToRadicals can be used to convert to explicit radicals.
Root[{f, x0}] represents an exact root of the general equation f[x]=0, which can be transcendental.
In Root[{f, x0}], x0 must be an approximate real or complex number such that exactly one root of f[x] lies within the numerical region defined by its precision.
Root[{f, x0, n}] represents n roots, counting multiplicity, that lie within the numerical region defined by the precision of x0.
N finds the approximate numerical value of a Root object.
Root[f, k] is treated as a numeric quantity if f contains no symbolic parameters.
Root by default isolates the complex roots of a polynomial using validated numerical methods. SetOptions[Root, ExactRootIsolation->True] will make Root use symbolic methods that are usually much slower.
EXAMPLES
Basic Examples 
Scope 