diff --git a/numpy/polynomial/chebyshev.py b/numpy/polynomial/chebyshev.py
index 836f473636e0..c37b2c6d623d 100644
--- a/numpy/polynomial/chebyshev.py
+++ b/numpy/polynomial/chebyshev.py
@@ -1743,7 +1743,8 @@ def chebroots(c):
     if len(c) == 2:
         return np.array([-c[0]/c[1]])
 
-    m = chebcompanion(c)
+    # rotated companion matrix reduces error
+    m = chebcompanion(c)[::-1,::-1]
     r = la.eigvals(m)
     r.sort()
     return r
diff --git a/numpy/polynomial/hermite.py b/numpy/polynomial/hermite.py
index dcd0a2b4d29a..3870d1054a4a 100644
--- a/numpy/polynomial/hermite.py
+++ b/numpy/polynomial/hermite.py
@@ -1476,7 +1476,8 @@ def hermroots(c):
     if len(c) == 2:
         return np.array([-.5*c[0]/c[1]])
 
-    m = hermcompanion(c)
+    # rotated companion matrix reduces error
+    m = hermcompanion(c)[::-1,::-1]
     r = la.eigvals(m)
     r.sort()
     return r
diff --git a/numpy/polynomial/hermite_e.py b/numpy/polynomial/hermite_e.py
index 48e5eab207f2..b12c0d792c98 100644
--- a/numpy/polynomial/hermite_e.py
+++ b/numpy/polynomial/hermite_e.py
@@ -1471,7 +1471,8 @@ def hermeroots(c):
     if len(c) == 2:
         return np.array([-c[0]/c[1]])
 
-    m = hermecompanion(c)
+    # rotated companion matrix reduces error
+    m = hermecompanion(c)[::-1,::-1]
     r = la.eigvals(m)
     r.sort()
     return r
diff --git a/numpy/polynomial/laguerre.py b/numpy/polynomial/laguerre.py
index 41d15142ae1f..e103dde92f28 100644
--- a/numpy/polynomial/laguerre.py
+++ b/numpy/polynomial/laguerre.py
@@ -1475,7 +1475,8 @@ def lagroots(c):
     if len(c) == 2:
         return np.array([1 + c[0]/c[1]])
 
-    m = lagcompanion(c)
+    # rotated companion matrix reduces error
+    m = lagcompanion(c)[::-1,::-1]
     r = la.eigvals(m)
     r.sort()
     return r
diff --git a/numpy/polynomial/legendre.py b/numpy/polynomial/legendre.py
index d56e2ae2c0e7..9eec9740d9c9 100644
--- a/numpy/polynomial/legendre.py
+++ b/numpy/polynomial/legendre.py
@@ -1505,7 +1505,8 @@ def legroots(c):
     if len(c) == 2:
         return np.array([-c[0]/c[1]])
 
-    m = legcompanion(c)
+    # rotated companion matrix reduces error
+    m = legcompanion(c)[::-1,::-1]
     r = la.eigvals(m)
     r.sort()
     return r
diff --git a/numpy/polynomial/polynomial.py b/numpy/polynomial/polynomial.py
index e3eb7ec5aaaa..afa330502602 100644
--- a/numpy/polynomial/polynomial.py
+++ b/numpy/polynomial/polynomial.py
@@ -1428,7 +1428,8 @@ def polyroots(c):
     if len(c) == 2:
         return np.array([-c[0]/c[1]])
 
-    m = polycompanion(c)
+    # rotated companion matrix reduces error
+    m = polycompanion(c)[::-1,::-1]
     r = la.eigvals(m)
     r.sort()
     return r