diff --git a/src/NumField/Elem.jl b/src/NumField/Elem.jl
index ebf8d41bd4..ce57fd9ae8 100644
--- a/src/NumField/Elem.jl
+++ b/src/NumField/Elem.jl
@@ -460,8 +460,7 @@ end
 function roots(f::PolyRingElem{<: NumFieldElem})
   lf = factor(f)
   @assert degree(unit(lf)) == 0
-  scale = inv(coeff(unit(lf), 0))
-  return elem_type(base_ring(f))[-constant_coefficient(x)*scale for x = keys(lf.fac) if degree(x) == 1]
+  return elem_type(base_ring(f))[-constant_coefficient(x)*inv(leading_coefficient(x)) for x = keys(lf.fac) if degree(x) == 1]
 end
 
 ################################################################################
diff --git a/test/NumField/Elem.jl b/test/NumField/Elem.jl
index 640f79d4d0..9e65b74967 100644
--- a/test/NumField/Elem.jl
+++ b/test/NumField/Elem.jl
@@ -245,3 +245,16 @@ end
   @test !isone(g^8)
   @test !isone(g^3)
 end
+
+# Issue with scaling of roots found by M. Zach
+begin
+  Qx, x = QQ["x"]
+  K, a = number_field(x^2 + x + 1, cached = false)
+  Ks, s = polynomial_ring(K, "s")
+  L, = number_field(s^8 + 6s^4 + 1)
+  Ly, y = L["y"]
+  h = -1//4*y^8 - 3//2*y^4 - 1//4
+  r = roots(h)
+  @test length(r) == 8
+  @test all(iszero, h.(r))
+end