Finds the roots of a polynomial.
ROOTS(coef, method)
coef 
 
Any series, the polynomial coefficients in descending powers (highest degree to lowest).  
method 
 
Optional. An integer, the root finding method:

A real or complex series, the roots of the polynomial.
r = roots({1, 1, 1})
r == {1.618034, 0.618034}
r[1] == phi
returns 1, demonstrating that for polynomial:
i.e. positive root of
roots({1, 2, 0})
returns {0, 2}, the roots of:
roots(poly({3, 2, 1}))
returns {3, 2, 1}, showing that roots and POLY are inverse functions within machine precision.
a := rand
x = 10..0.01..10
W1: roots({a, 1, 1, 1})
W2: xy(W1, zeros(length(W1),1));points;setsym(14)
W3: a*x^3 + x^2  x  1;overp(W2, lred)
W3 displays a cubic of the form:
The roots of the cubic are overplotted in red and displayed as solid circles.
Executing the statement a := rand creates a new polynomial that is automatically updated in W3. A zoomed portion of the graph below shows the cubic nature of the location of the roots.
By default, ROOTS calculates the roots of a polynomial by finding the eigenvalues of the companion matrix for the corresponding characteristic polynomial.
roots(a) finds the roots of:
where the coefficients are ordered from highest power to lowest power.
If a lower order term does not exist, the corresponding coefficient must be set to 0.
See POLYROOT to determine the roots of a polynomial in ascending powers (lowest degree to highest).