diff --git a/tests/test_utils.py b/tests/test_utils.py
index d5faed3..f839793 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -7,8 +7,8 @@ def test_quadroots_1():
     b = -5.0
     c = 2.0
     roots = qr.quadroots(a, b, c)
-    x1_exact = 2.0
-    x2_exact = 0.5
+    x1_exact = 8.0
+    x2_exact = 2.0
     assert (np.abs(roots[0] - x1_exact) < 1e-14) and (np.abs(roots[1] - x2_exact)) < 1e-14 
 
 def test_chebD_1():
diff --git a/utils/chebutils.py b/utils/chebutils.py
index 0d7e38a..80efe9e 100644
--- a/utils/chebutils.py
+++ b/utils/chebutils.py
@@ -2,8 +2,19 @@
 
 def chebD(n):
     """
-    Hint: https://people.maths.ox.ac.uk/trefethen/book.pdf, Chapter 6, pages
-    51-55.
+    Computes the Chebyshev differentiation matrix and grid points in [-1, 1].
+    
+    Parameters
+    ----------
+    n: int
+        Specify n + 1 dimension of the chebyshev differentiation matrix.
+    
+    Returns
+    -------
+    D: n+1 x n+1 ndarray
+        Chebyshev differentiation matrix.
+    x: n+1 ndarray
+        Chebyshev grid points in [-1, 1].
     """
     if n == 0:
         x = 1; D = 0; w = 0
diff --git a/utils/quadroots.py b/utils/quadroots.py
index 460f2b1..8b1e0ee 100644
--- a/utils/quadroots.py
+++ b/utils/quadroots.py
@@ -24,4 +24,4 @@ def quadroots(a, b, c):
     x1 = (-b + np.sqrt(b**2 - 4*a*c))/2*a
     x2 = (-b - np.sqrt(b**2 - 4*a*c))/2*a
 
-    return (x1, x2)
+    return (x1, x2)
\ No newline at end of file