# Root finding package with array of polynomials?

**URL:** <https://discourse.julialang.org/t/root-finding-package-with-array-of-polynomials/74061>\
**Category:** General Usage\
**Created:** [January 4, 2022, 9:27pm UTC](https://discourse.julialang.org/t/root-finding-package-with-array-of-polynomials/74061 "2022-01-04T21:27:45Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![DeepQ](https://avatars.discourse-cdn.com/v4/letter/d/2bfe46/32.png) [@DeepQ](https://discourse.julialang.org/u/DeepQ)\
**Post date:** [January 4, 2022, 9:27pm UTC](https://discourse.julialang.org/t/root-finding-package-with-array-of-polynomials/74061/1 "2022-01-04T21:27:45Z")

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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}

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**Author:** ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)\
**Post date:** [January 4, 2022, 9:37pm UTC](https://discourse.julialang.org/t/root-finding-package-with-array-of-polynomials/74061/2 "2022-01-04T21:37:37Z")

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A package specifically for systems of polynomial equations: [https://www.juliahomotopycontinuation.org/](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.)