# Using Symbolics & Nemo; Unexpected roots of simple 2nd degree polynomial equation

**URL:** https://discourse.julialang.org/t/using-symbolics-nemo-unexpected-roots-of-simple-2nd-degree-polynomial-equation/127281
**Category:** New to Julia
**Tags:** question
**Created:** [March 23, 2025, 2:01pm UTC](https://discourse.julialang.org/t/using-symbolics-nemo-unexpected-roots-of-simple-2nd-degree-polynomial-equation/127281 "2025-03-23T14:01:58Z")
**Posts on this page:** 3
**Page:** 1

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### Author: ![theo.bruelhart](https://avatars.discourse-cdn.com/v4/letter/t/5f9b8f/32.png) [@theo.bruelhart](https://discourse.julialang.org/u/theo.bruelhart)
#### Post date: [March 23, 2025, 2:01pm UTC](https://discourse.julialang.org/t/using-symbolics-nemo-unexpected-roots-of-simple-2nd-degree-polynomial-equation/127281/1 "2025-03-23T14:01:58Z")

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**[Issue]**  
Unexpected roots of simple 2nd degree polynomial equation using Symbolics.jl and Nemo.jl

Obtained results: [(1//2)\*√(4y), (-1//2)\*√(4y)]  
Expected result: [√(y), -√(y)]

**[Environment]**

- Linux thinkpad 6.1.0-32-amd64 #1 SMP PREEMPT\_DYNAMIC Debian 6.1.129-1 (2025-03-06) x86\_64 GNU/Linux
- julia version 1.11.3
- nemo.jl version v0.48.4
- symbolics.jl version v6.33.1

**[Code]**

```julia
using Pkg
Pkg.add("Symbolics"); using Symbolics
Pkg.add("Nemo"); using Nemo

@variables x, y
exp1 = x^2 ~ y
roots = symbolic_solve(exp1,x)
println(roots)

```

**[Output]**  
`SymbolicUtils.BasicSymbolic{Real}[(1//2)*√(4y), (-1//2)*√(4y)]`

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<div class="post-metadata">

### Author: ![Datseris](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/datseris/32/13406_2.png) [@Datseris](https://discourse.julialang.org/u/Datseris)
#### Post date: [March 23, 2025, 2:49pm UTC](https://discourse.julialang.org/t/using-symbolics-nemo-unexpected-roots-of-simple-2nd-degree-polynomial-equation/127281/2 "2025-03-23T14:49:29Z")

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Shouldn’t the answer be +/- sqrt(y)…? Which is what symbolics finds as the 1//2 and the sqrt(4) cancel out.

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<div class="post-metadata">

### Author: ![theo.bruelhart](https://avatars.discourse-cdn.com/v4/letter/t/5f9b8f/32.png) [@theo.bruelhart](https://discourse.julialang.org/u/theo.bruelhart)
#### Post date: [March 23, 2025, 8:10pm UTC](https://discourse.julialang.org/t/using-symbolics-nemo-unexpected-roots-of-simple-2nd-degree-polynomial-equation/127281/3 "2025-03-23T20:10:40Z")

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You are entirely correct, and I value your quick reply. I am uncertain how I failed to recognize this (obvious) fact; I must have been fatigued while addressing this equation.

I have corrected this post and opened a new query [1] to explore how to simplify the output further, specifically why it is not presented in its simplest form and if there is a way to enforce maximum algebraic reduction.

[1] [Achieving Maximum Algebraic Simplification in Symbolic Computation](https://discourse.julialang.org/t/achieving-maximum-algebraic-simplification-in-symbolic-computation/127288)