diff --git a/tests/test_utils.py b/tests/test_utils.py
index d5faed3..f48651e 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -12,4 +12,8 @@ def test_quadroots_1():
     assert (np.abs(roots[0] - x1_exact) < 1e-14) and (np.abs(roots[1] - x2_exact)) < 1e-14 
 
 def test_chebD_1():
-    pass
+    n=2
+    exact = [[ 1.5, -2.0,  0.5], [ 0.5,  0.0,  -0.5], [-0.5,  2.0,  -1.5]]
+    diffMatrix, grid = ch.chebD(n)
+    checkArr = diffMatrix - exact
+    assert(np.all(checkArr < 1e-14))
diff --git a/utils/chebutils.py b/utils/chebutils.py
index 0d7e38a..cf47567 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 a spectral differentiation matrix and Chebysev grid
+    
+    Parameters
+    ----------
+    n: <int>
+        An integer defining the number of grid points (n+1)
+    
+    Returns
+    -------
+    D: (n+1)x(n+1) matrix
+        differentiation matrix
+    x: (n+1)-d array
+        Chebysev grid
     """
     if n == 0:
         x = 1; D = 0; w = 0
diff --git a/utils/quadroots.py b/utils/quadroots.py
index 460f2b1..4cb77ed 100644
--- a/utils/quadroots.py
+++ b/utils/quadroots.py
@@ -21,7 +21,7 @@ def quadroots(a, b, c):
         Roots of the equation.
     """
 
-    x1 = (-b + np.sqrt(b**2 - 4*a*c))/2*a
-    x2 = (-b - np.sqrt(b**2 - 4*a*c))/2*a
+    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)