# Root finding package with array of polynomials?

I have a function defined like:

f(x) = a_1x^2+a_2x+a_3

I know that I can find its roots using Roots.jl package. How can I find its roots if its coefficients are a (3,n) matrix instead of just 3 numbers? The matrix is defined like:
\begin{bmatrix} a_{1,1} & ...& a_{1,n}\\ a_{2,1} &...& a_{2,n}\\ a_{3,1} &...& a_{3,n}\end{bmatrix}

A package specifically for systems of polynomial equations: https://www.juliahomotopycontinuation.org/

(You can also use generic nonlinear root-finding methods, of course, like Newton’s method, but those require an initial guess for a root in order to converge. Specialized methods for polynomial systems can find all of the roots much more reliably.)

2 Likes